Details

Time bar (total: 9.3s)

sample43.0ms

Algorithm
intervals
Results
23.0ms256×body80valid

simplify42.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
05216
113116
234216
3120216
4500216
done500216

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 2.0b

localize29.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (sin ky) 2.0)
0.3b
(pow (sin kx) 2.0)
2.5b
(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
6.9b
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

rewrite91.0ms

Algorithm
rewrite-expression-head
Rules
19×add-sqr-sqrt
18×add-exp-log
17×*-un-lft-identity
16×unpow-prod-down
13×add-cube-cbrt
11×associate-*l*
7×pow1
6×pow-unpow prod-exp add-cbrt-cube
5×associate-*r* pow-exp
4×expm1-log1p-u log1p-expm1-u add-log-exp sqr-pow
3×pow-to-exp times-frac sqrt-prod unswap-sqr
2×pow-pow flip3-+ sqrt-div associate-*r/ div-exp flip-+ distribute-lft-out
1×distribute-rgt-in rem-sqrt-square distribute-lft-in sqrt-pow1 pow1/2 *-commutative cbrt-unprod div-inv
Counts
4 → 94
Calls
4 calls:
3.0ms
(pow (sin ky) 2.0)
3.0ms
(pow (sin kx) 2.0)
75.0ms
(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
6.0ms
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

series941.0ms

Counts
4 → 12
Calls
4 calls:
102.0ms
(pow (sin ky) 2.0)
101.0ms
(pow (sin kx) 2.0)
389.0ms
(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
348.0ms
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

simplify64.0ms

Counts
106 → 106
Iterations

Useful iterations: 1 (17.0ms)

IterNodesCost
0489887
11950857
25002857
done5002857

prune450.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 1.9b

localize29.0ms

Local error

Found 4 expressions with local error:

6.9b
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
8.3b
(cbrt (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
8.3b
(cbrt (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
8.3b
(cbrt (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
18×cbrt-prod
12×add-sqr-sqrt sqrt-prod
11×add-cube-cbrt *-un-lft-identity
8×sqrt-div
6×cbrt-div
5×pow1
4×add-exp-log expm1-log1p-u flip3-+ add-cbrt-cube flip-+ log1p-expm1-u add-log-exp
3×pow1/3
1×rem-sqrt-square sqrt-pow1 pow1/2
Counts
4 → 71
Calls
4 calls:
5.0ms
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
4.0ms
(cbrt (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
4.0ms
(cbrt (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
4.0ms
(cbrt (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))

series1.3s

Counts
4 → 12
Calls
4 calls:
344.0ms
(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
316.0ms
(cbrt (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
313.0ms
(cbrt (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
315.0ms
(cbrt (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))

simplify93.0ms

Counts
83 → 83
Iterations

Useful iterations: 2 (15.0ms)

IterNodesCost
01351468
14321382
223571376
350011376
done50011376

prune495.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 1.9b

localize37.0ms

Local error

Found 4 expressions with local error:

8.3b
(cbrt (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
8.3b
(cbrt (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
8.3b
(cbrt (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
8.3b
(cbrt (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
24×cbrt-prod
12×add-sqr-sqrt add-cube-cbrt *-un-lft-identity sqrt-prod
8×cbrt-div sqrt-div
4×pow1 add-exp-log expm1-log1p-u flip3-+ pow1/3 add-cbrt-cube flip-+ log1p-expm1-u add-log-exp
Counts
4 → 72
Calls
4 calls:
4.0ms
(cbrt (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
4.0ms
(cbrt (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
4.0ms
(cbrt (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
4.0ms
(cbrt (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))

series1.3s

Counts
4 → 12
Calls
4 calls:
315.0ms
(cbrt (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
312.0ms
(cbrt (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
318.0ms
(cbrt (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
312.0ms
(cbrt (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))

simplify87.0ms

Counts
84 → 84
Iterations

Useful iterations: 2 (15.0ms)

IterNodesCost
01261592
14111492
222841484
350011484
done50011484

prune557.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 1.9b

localize42.0ms

Local error

Found 4 expressions with local error:

8.3b
(cbrt (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
8.3b
(cbrt (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
8.3b
(cbrt (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
8.3b
(cbrt (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
24×cbrt-prod
12×add-sqr-sqrt add-cube-cbrt *-un-lft-identity sqrt-prod
8×cbrt-div sqrt-div
4×pow1 add-exp-log expm1-log1p-u flip3-+ pow1/3 add-cbrt-cube flip-+ log1p-expm1-u add-log-exp
Counts
4 → 72
Calls
4 calls:
4.0ms
(cbrt (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
4.0ms
(cbrt (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
4.0ms
(cbrt (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
4.0ms
(cbrt (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))

series1.4s

Counts
4 → 12
Calls
4 calls:
314.0ms
(cbrt (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
469.0ms
(cbrt (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
320.0ms
(cbrt (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
319.0ms
(cbrt (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))

simplify86.0ms

Counts
84 → 84
Iterations

Useful iterations: 2 (15.0ms)

IterNodesCost
01261592
14111492
222841484
350011484
done50011484

prune556.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 1.9b

regimes544.0ms

Accuracy

0% (0.4b remaining)

Error of 1.8b against oracle of 1.4b and baseline of 1.8b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03243
13243
done3243

end0.0ms

sample1.1s

Algorithm
intervals
Results
747.0ms8000×body80valid