Details

Time bar (total: 26.4s)

sample86.0ms

Algorithm
intervals
Results
51.0ms256×body80valid

simplify5.2s

Counts
1 → 1
Iterations

Useful iterations: 2 (50.0ms)

IterNodesCost
02229
15229
213128
333028
4115228
5477228
done500028

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.2b

localize32.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (sin ky) 2.0)
0.3b
(/ 1.0 (sqrt (fma (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) 1.0)))
1.5b
(fma (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) 1.0)
8.0b
(sqrt (fma (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) 1.0))

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
23×add-sqr-sqrt
22×add-cube-cbrt *-un-lft-identity
18×times-frac
15×sqrt-prod
7×add-exp-log
6×pow1 associate-/r* add-cbrt-cube
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×unpow-prod-down pow-unpow associate-/l*
1×cbrt-undiv pow-to-exp rem-sqrt-square pow-pow frac-2neg sqrt-pow1 pow1/2 div-exp pow-exp clear-num fma-udef div-inv sqr-pow
Counts
4 → 85
Calls
4 calls:
16.0ms
(pow (sin ky) 2.0)
6.0ms
(/ 1.0 (sqrt (fma (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) 1.0)))
0.0ms
(fma (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) 1.0)
5.0ms
(sqrt (fma (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) 1.0))

series1.7s

Counts
4 → 12
Calls
4 calls:
165.0ms
(pow (sin ky) 2.0)
652.0ms
(/ 1.0 (sqrt (fma (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) 1.0)))
349.0ms
(fma (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) 1.0)
571.0ms
(sqrt (fma (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) 1.0))

simplify1.5s

Counts
97 → 97
Iterations

Useful iterations: done (1.5s)

IterNodesCost
01682499
13172299
27102094
319782088
done50012070

prune757.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 1.2b

localize93.0ms

Local error

Found 4 expressions with local error:

4.2b
(cbrt (/ 1.0 (sqrt (fma (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) 1.0))))
8.0b
(sqrt (fma (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) 1.0))
8.0b
(sqrt (fma (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) 1.0))
8.0b
(sqrt (fma (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) 1.0))

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
23×add-sqr-sqrt
22×cbrt-prod
20×add-cube-cbrt *-un-lft-identity
18×times-frac sqrt-prod
7×pow1
4×add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
3×rem-sqrt-square sqrt-pow1 pow1/2
1×cbrt-div pow1/3 div-inv
Counts
4 → 78
Calls
4 calls:
21.0ms
(cbrt (/ 1.0 (sqrt (fma (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) 1.0))))
3.0ms
(sqrt (fma (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) 1.0))
3.0ms
(sqrt (fma (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) 1.0))
3.0ms
(sqrt (fma (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) 1.0))

series2.3s

Counts
4 → 12
Calls
4 calls:
677.0ms
(cbrt (/ 1.0 (sqrt (fma (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) 1.0))))
548.0ms
(sqrt (fma (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) 1.0))
497.0ms
(sqrt (fma (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) 1.0))
537.0ms
(sqrt (fma (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) 1.0))

simplify3.5s

Counts
90 → 90
Iterations

Useful iterations: done (3.5s)

IterNodesCost
01422805
12362563
24632356
311182345
435952321
done50002297

prune730.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 1.2b

localize105.0ms

Local error

Found 4 expressions with local error:

4.2b
(cbrt (/ 1.0 (sqrt (fma (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) 1.0))))
8.0b
(sqrt (fma (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) 1.0))
8.0b
(sqrt (fma (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) 1.0))
8.0b
(sqrt (fma (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) 1.0))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
23×add-sqr-sqrt
22×cbrt-prod
20×add-cube-cbrt *-un-lft-identity
18×times-frac sqrt-prod
7×pow1
4×add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
3×rem-sqrt-square sqrt-pow1 pow1/2
1×cbrt-div pow1/3 div-inv
Counts
4 → 78
Calls
4 calls:
6.0ms
(cbrt (/ 1.0 (sqrt (fma (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) 1.0))))
3.0ms
(sqrt (fma (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) 1.0))
3.0ms
(sqrt (fma (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) 1.0))
3.0ms
(sqrt (fma (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) 1.0))

series2.4s

Counts
4 → 12
Calls
4 calls:
715.0ms
(cbrt (/ 1.0 (sqrt (fma (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) 1.0))))
566.0ms
(sqrt (fma (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) 1.0))
532.0ms
(sqrt (fma (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) 1.0))
540.0ms
(sqrt (fma (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)) 1.0))

simplify3.3s

Counts
90 → 90
Iterations

Useful iterations: done (3.3s)

IterNodesCost
01422805
12362563
24632356
311182345
435952321
done50002297

prune892.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 1.2b

localize7.0ms

rewrite0.0ms

Algorithm
rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms

Counts
0 → 0

simplify0.0ms

Counts
0 → 0
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
000
done00

prune0.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 1.2b

regimes559.0ms

Accuracy

0% (0.5b remaining)

Error of 1.8b against oracle of 1.3b and baseline of 1.8b

bsearch0.0ms

simplify7.0ms

Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
02475
12875
done2875

end0.0ms

sample3.2s

Algorithm
intervals
Results
2.7s7999×body80valid
1.0ms1×body160valid