Details

Time bar (total: 56.9s)

sample592.0ms

Algorithm
intervals
Results
557.0ms256×body80valid

simplify264.0ms

Calls
1 calls:
Slowest
263.0ms
(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: 2.6b

localize60.0ms

Local error

Found 4 expressions with local error:

11.7b
(sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))
2.6b
(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)))
0.2b
(* (sin kx) (sin kx))

rewrite34.0ms

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
Calls
4 calls:
Slowest
23.0ms
(* (sin kx) (sin kx))
5.0ms
(/ 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)

series990.0ms

Calls
4 calls:
Slowest
448.0ms
(/ 1/2 (sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)))
333.0ms
(sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))
190.0ms
(fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)
20.0ms
(* (sin kx) (sin kx))

simplify17.6s

Calls
86 calls:
Slowest
454.0ms
(* (sqrt (+ (* 4 (pow (sin ky) 2)) (* 4 (pow (sin kx) 2)))) (/ l Om))
449.0ms
(- (log 1/2) (log (sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))))
446.0ms
(/ (* (cbrt 1/2) (cbrt 1/2)) (sqrt (sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))))
427.0ms
(/ 1/2 (sqrt (sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))))
427.0ms
(/ (cbrt 1/2) (sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)))

prune2.1s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 1.0b

localize83.0ms

Local error

Found 4 expressions with local error:

11.7b
(sqrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1))
3.0b
(/ (* (sin ky) l) Om)
3.0b
(/ (* (sin ky) l) Om)
1.4b
(/ (* l (sin kx)) Om)

rewrite42.0ms

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
Calls
4 calls:
Slowest
16.0ms
(/ (* l (sin kx)) Om)
12.0ms
(/ (* (sin ky) l) Om)
11.0ms
(/ (* (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))

series581.0ms

Calls
4 calls:
Slowest
336.0ms
(sqrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1))
100.0ms
(/ (* (sin ky) l) Om)
77.0ms
(/ (* l (sin kx)) Om)
68.0ms
(/ (* (sin ky) l) Om)

simplify4.5s

Calls
55 calls:
Slowest
435.0ms
(* (sqrt (+ (* 4 (pow (sin ky) 2)) (* 4 (pow (sin kx) 2)))) (/ l Om))
388.0ms
(* (sqrt (+ (* 4 (pow (sin ky) 2)) (* 4 (pow (sin kx) 2)))) (/ l Om))
366.0ms
(sqrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1))
304.0ms
(fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1)
272.0ms
(sqrt (sqrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1)))

prune2.3s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 1.0b

localize117.0ms

Local error

Found 4 expressions with local error:

11.7b
(sqrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1))
11.7b
(sqrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1))
11.7b
(sqrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1))
6.9b
(cbrt (sqrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1)))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt sqrt-prod
9×*-un-lft-identity add-cube-cbrt
7×pow1
6×cbrt-prod
4×expm1-log1p-u add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
3×rem-sqrt-square sqrt-pow1 pow1/2
1×pow1/3
Calls
4 calls:
Slowest
3.0ms
(sqrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1))
3.0ms
(sqrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1))
2.0ms
(sqrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1))
2.0ms
(cbrt (sqrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1)))

series1.4s

Calls
4 calls:
Slowest
362.0ms
(sqrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1))
358.0ms
(sqrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1))
350.0ms
(sqrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1))
336.0ms
(cbrt (sqrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1)))

simplify8.2s

Calls
33 calls:
Slowest
494.0ms
(* (sqrt (+ (* 4 (pow (sin ky) 2)) (* 4 (pow (sin kx) 2)))) (/ l Om))
475.0ms
(* (sqrt (+ (* 4 (pow (sin ky) 2)) (* 4 (pow (sin kx) 2)))) (/ l Om))
433.0ms
(* (sqrt (+ (* 4 (pow (sin ky) 2)) (* 4 (pow (sin kx) 2)))) (/ l Om))
419.0ms
(* (sqrt (+ (* 4 (pow (sin ky) 2)) (* 4 (pow (sin kx) 2)))) (/ l Om))
416.0ms
(* (sqrt (+ (* 4 (pow (sin ky) 2)) (* 4 (pow (sin kx) 2)))) (/ l Om))

prune1.8s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 1.0b

localize120.0ms

Local error

Found 4 expressions with local error:

29.6b
(posit16->real (real->posit16 (cbrt (sqrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1)))))
11.7b
(sqrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1))
11.7b
(sqrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1))
11.7b
(sqrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1))

rewrite4.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
9×sqrt-prod
7×pow1 *-un-lft-identity add-cube-cbrt
4×expm1-log1p-u add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
3×rem-sqrt-square sqrt-pow1 pow1/2
1×remove-posit16
Calls
4 calls:
Slowest
1.0ms
(sqrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1))
1.0ms
(sqrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1))
1.0ms
(sqrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1))
0.0ms
(posit16->real (real->posit16 (cbrt (sqrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1)))))

series1.4s

Calls
4 calls:
Slowest
381.0ms
(sqrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1))
381.0ms
(sqrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1))
343.0ms
(sqrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1))
299.0ms
(posit16->real (real->posit16 (cbrt (sqrt (fma 4 (+ (* (/ (* (sin ky) l) Om) (/ (* (sin ky) l) Om)) (* (/ (* l (sin kx)) Om) (/ (* l (sin kx)) Om))) 1)))))

simplify7.2s

Calls
28 calls:
Slowest
470.0ms
(* (sqrt (+ (* 4 (pow (sin ky) 2)) (* 4 (pow (sin kx) 2)))) (/ l Om))
445.0ms
(* (sqrt (+ (* 4 (pow (sin ky) 2)) (* 4 (pow (sin kx) 2)))) (/ l Om))
431.0ms
(* (sqrt (+ (* 4 (pow (sin ky) 2)) (* 4 (pow (sin kx) 2)))) (/ l Om))
429.0ms
(* (sqrt (+ (* 4 (pow (sin ky) 2)) (* 4 (pow (sin kx) 2)))) (/ l Om))
413.0ms
(* (sqrt (+ (* 4 (pow (sin ky) 2)) (* 4 (pow (sin kx) 2)))) (/ l Om))

prune3.0s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 1.0b

regimes717.0ms

Accuracy

0% (0.0b remaining)

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

bsearch19.0ms

end0.0ms

sample3.6s

Algorithm
intervals
Results
3.4s8000×body80valid