Details

Time bar (total: 1.5m)

sample87.0ms

Algorithm
intervals
Results
60.0ms256×body80valid

simplify293.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
292.0ms
(sqrt (* (/ 1 2) (+ 1 (/ 1 (sqrt (+ 1 (* (pow (/ (* 2 l) Om) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))))

prune34.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.2b

localize50.0ms

Local error

Found 4 expressions with local error:

9.2b
(sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))
1.7b
(fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)
0.5b
(/ 1/2 (sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)))
0.3b
(* (sin kx) (sin kx))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
27×add-sqr-sqrt
24×*-un-lft-identity add-cube-cbrt
18×times-frac
15×sqrt-prod
12×pow1
8×add-cbrt-cube add-exp-log
6×associate-/r*
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×swap-sqr associate-*r* associate-*l* associate-/l*
1×pow2 cbrt-undiv rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow-plus pow1/2 div-exp pow-prod-down prod-exp pow-sqr *-commutative pow-prod-up cbrt-unprod fma-udef sqr-sin div-inv sin-mult unswap-sqr
Counts
4 → 99
Calls
4 calls:
Slowest
12.0ms
(* (sin kx) (sin kx))
7.0ms
(/ 1/2 (sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)))
3.0ms
(sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))
0.0ms
(fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)

series984.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
423.0ms
(/ 1/2 (sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)))
338.0ms
(sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))
189.0ms
(fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)
34.0ms
(* (sin kx) (sin kx))

simplify16.8s

Counts
86 → 111
Calls
86 calls:
Slowest
775.0ms
(/ (cbrt 1/2) (sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)))
444.0ms
(* (sqrt (+ (* 4 (pow (sin ky) 2)) (* 4 (pow (sin kx) 2)))) (/ l Om))
434.0ms
(sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))
412.0ms
(- (log 1/2) (log (sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))))
409.0ms
(/ (* (cbrt 1/2) (cbrt 1/2)) (sqrt (* (cbrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)) (cbrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)))))

prune1.9s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.4b

localize69.0ms

Local error

Found 4 expressions with local error:

9.2b
(sqrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1))
3.5b
(/ (* (sin ky) l) Om)
3.5b
(/ (* (sin ky) l) Om)
3.0b
(/ (* l (sin kx)) Om)

rewrite54.0ms

Algorithm
rewrite-expression-head
Rules
19×add-cbrt-cube add-exp-log
12×add-sqr-sqrt
11×*-un-lft-identity add-cube-cbrt
9×associate-/r* times-frac
6×cbrt-undiv div-exp
5×pow1
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×clear-num frac-2neg prod-exp sqrt-prod cbrt-unprod div-inv associate-/l*
1×rem-sqrt-square sqrt-pow1 pow1/2
Counts
4 → 88
Calls
4 calls:
Slowest
23.0ms
(/ (* (sin ky) l) Om)
15.0ms
(/ (* l (sin kx)) Om)
14.0ms
(/ (* (sin ky) l) Om)
1.0ms
(sqrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1))

series574.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
354.0ms
(sqrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1))
85.0ms
(/ (* (sin ky) l) Om)
70.0ms
(/ (* l (sin kx)) Om)
65.0ms
(/ (* (sin ky) l) Om)

simplify4.5s

Counts
55 → 100
Calls
55 calls:
Slowest
411.0ms
(* (sqrt (+ (* 4 (pow (sin ky) 2)) (* 4 (pow (sin kx) 2)))) (/ l Om))
389.0ms
(* (sqrt (+ (* 4 (pow (sin ky) 2)) (* 4 (pow (sin kx) 2)))) (/ l Om))
374.0ms
(sqrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1))
313.0ms
(sqrt (sqrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1)))
304.0ms
(- (/ (* kx l) Om) (* 1/6 (/ (* (pow kx 3) l) Om)))

prune1.9s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.4b

localize92.0ms

Local error

Found 4 expressions with local error:

9.2b
(sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))
2.1b
(log (exp (/ 1/2 (sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)))))
1.7b
(fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)
0.5b
(/ 1/2 (sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
36×times-frac
35×add-sqr-sqrt
34×*-un-lft-identity add-cube-cbrt
24×sqrt-prod
23×log-pow
22×exp-prod
6×pow1 associate-/r* add-cbrt-cube add-exp-log
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×log-prod associate-/l*
2×div-inv
1×cbrt-undiv rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 div-exp rem-log-exp fma-udef
Counts
4 → 106
Calls
4 calls:
Slowest
13.0ms
(log (exp (/ 1/2 (sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)))))
9.0ms
(/ 1/2 (sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)))
3.0ms
(sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))
0.0ms
(fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)

series1.5s

Counts
4 → 12
Calls
4 calls:
Slowest
503.0ms
(/ 1/2 (sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)))
499.0ms
(log (exp (/ 1/2 (sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)))))
328.0ms
(sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))
180.0ms
(fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)

simplify25.4s

Counts
88 → 118
Calls
88 calls:
Slowest
893.0ms
(log (* (cbrt (exp (/ 1/2 (sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))))) (cbrt (exp (/ 1/2 (sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)))))))
561.0ms
(sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))
481.0ms
(/ 1/2 (sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)))
457.0ms
(/ (sqrt 1/2) (sqrt (cbrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))))
457.0ms
(/ (cbrt 1/2) (sqrt (sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))))

prune2.4s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.4b

localize91.0ms

Local error

Found 4 expressions with local error:

9.2b
(sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))
9.2b
(sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))
2.9b
(log (sqrt (exp (/ 1/2 (sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))))))
2.9b
(log (sqrt (exp (/ 1/2 (sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))))))

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
50×log-pow
48×sqrt-pow1
44×exp-prod
38×add-sqr-sqrt
36×*-un-lft-identity times-frac add-cube-cbrt
30×sqrt-prod
12×log-prod
10×pow1
6×add-exp-log
4×expm1-log1p-u add-cbrt-cube pow1/2 insert-posit16 log1p-expm1-u add-log-exp
2×rem-sqrt-square rem-log-exp div-inv
Counts
4 → 116
Calls
4 calls:
Slowest
15.0ms
(log (sqrt (exp (/ 1/2 (sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))))))
14.0ms
(log (sqrt (exp (/ 1/2 (sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))))))
3.0ms
(sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))
2.0ms
(sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))

series1.3s

Counts
4 → 12
Calls
4 calls:
Slowest
333.0ms
(sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))
329.0ms
(log (sqrt (exp (/ 1/2 (sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))))))
311.0ms
(log (sqrt (exp (/ 1/2 (sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))))))
310.0ms
(sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))

simplify25.8s

Counts
82 → 128
Calls
82 calls:
Slowest
757.0ms
(/ (/ (cbrt 1/2) (sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))) 2)
497.0ms
(/ (/ (cbrt 1/2) (sqrt (sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)))) 2)
451.0ms
(/ (/ (sqrt 1/2) (sqrt (cbrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)))) 2)
444.0ms
(/ (/ 1/2 (sqrt (cbrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)))) 2)
441.0ms
(* (sqrt (+ (* 4 (pow (sin ky) 2)) (* 4 (pow (sin kx) 2)))) (/ l Om))

prune2.9s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.4b

regimes437.0ms

Accuracy

0% (0.0b remaining)

Error of 0.6b against oracle of 0.6b and baseline of 0.6b

bsearch9.0ms

end0.0ms

sample3.8s

Algorithm
intervals
Results
3.5s8000×body80valid