Details

Time bar (total: 33.8s)

sample164.0ms

Algorithm
intervals
Results
105.0ms256×body80valid

simplify768.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
766.0ms
(sqrt (* (/ 1 2) (+ 1 (/ 1 (sqrt (+ 1 (* (pow (/ (* 2 l) Om) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))))

prune37.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.6b

localize68.0ms

Local error

Found 4 expressions with local error:

8.5b
(sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))
1.2b
(fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)
0.3b
(* (sin kx) (sin kx))
0.2b
(fma (sin ky) (sin ky) (* (sin kx) (sin kx)))

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt pow1
9×*-un-lft-identity add-cube-cbrt
6×add-cbrt-cube add-exp-log
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×swap-sqr associate-*r* associate-*l* sqrt-prod
2×fma-udef
1×pow2 rem-sqrt-square sqrt-pow1 pow-plus pow1/2 pow-prod-down prod-exp pow-sqr *-commutative pow-prod-up cbrt-unprod sqr-sin sin-mult unswap-sqr
Counts
4 → 68
Calls
4 calls:
Slowest
25.0ms
(* (sin kx) (sin kx))
3.0ms
(sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))
0.0ms
(fma (sin ky) (sin ky) (* (sin kx) (sin kx)))
0.0ms
(fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)

series697.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
362.0ms
(sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))
212.0ms
(fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)
101.0ms
(fma (sin ky) (sin ky) (* (sin kx) (sin kx)))
22.0ms
(* (sin kx) (sin kx))

simplify3.6s

Counts
40 → 80
Calls
40 calls:
Slowest
496.0ms
(* (sqrt (+ (* 4 (pow (sin ky) 2)) (* 4 (pow (sin kx) 2)))) (/ l Om))
411.0ms
(sqrt (sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)))
402.0ms
(sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))
395.0ms
(* (sqrt (+ (* 4 (pow (sin ky) 2)) (* 4 (pow (sin kx) 2)))) (/ l Om))
340.0ms
(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))))

prune1.5s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.3b

localize81.0ms

Local error

Found 4 expressions with local error:

41.1b
(posit16->real (real->posit16 (fma (sin ky) (sin ky) (* (sin kx) (sin kx)))))
8.5b
(sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (posit16->real (real->posit16 (fma (sin ky) (sin ky) (* (sin kx) (sin kx))))) 1))
1.2b
(fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (posit16->real (real->posit16 (fma (sin ky) (sin ky) (* (sin kx) (sin kx))))) 1)
0.3b
(* (sin kx) (sin kx))

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt pow1
9×*-un-lft-identity add-cube-cbrt
6×add-cbrt-cube add-exp-log
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×swap-sqr associate-*r* associate-*l* sqrt-prod
1×pow2 rem-sqrt-square sqrt-pow1 pow-plus pow1/2 pow-prod-down prod-exp pow-sqr *-commutative pow-prod-up cbrt-unprod fma-udef sqr-sin remove-posit16 sin-mult unswap-sqr
Counts
4 → 68
Calls
4 calls:
Slowest
30.0ms
(* (sin kx) (sin kx))
2.0ms
(sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (posit16->real (real->posit16 (fma (sin ky) (sin ky) (* (sin kx) (sin kx))))) 1))
0.0ms
(fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (posit16->real (real->posit16 (fma (sin ky) (sin ky) (* (sin kx) (sin kx))))) 1)
0.0ms
(posit16->real (real->posit16 (fma (sin ky) (sin ky) (* (sin kx) (sin kx)))))

series591.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
316.0ms
(sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (posit16->real (real->posit16 (fma (sin ky) (sin ky) (* (sin kx) (sin kx))))) 1))
182.0ms
(fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (posit16->real (real->posit16 (fma (sin ky) (sin ky) (* (sin kx) (sin kx))))) 1)
73.0ms
(posit16->real (real->posit16 (fma (sin ky) (sin ky) (* (sin kx) (sin kx)))))
19.0ms
(* (sin kx) (sin kx))

simplify3.5s

Counts
41 → 80
Calls
41 calls:
Slowest
469.0ms
(* (sqrt (+ (* 4 (pow (sin ky) 2)) (* 4 (pow (sin kx) 2)))) (/ l Om))
459.0ms
(* (sqrt (+ (* 4 (pow (sin ky) 2)) (* 4 (pow (sin kx) 2)))) (/ l Om))
415.0ms
(sqrt (* (cbrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (posit16->real (real->posit16 (fma (sin ky) (sin ky) (* (sin kx) (sin kx))))) 1)) (cbrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (posit16->real (real->posit16 (fma (sin ky) (sin ky) (* (sin kx) (sin kx))))) 1))))
372.0ms
(fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (posit16->real (real->posit16 (fma (sin ky) (sin ky) (* (sin kx) (sin kx))))) 1)
340.0ms
(sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (posit16->real (real->posit16 (fma (sin ky) (sin ky) (* (sin kx) (sin kx))))) 1))

prune2.4s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.3b

localize73.0ms

Local error

Found 4 expressions with local error:

13.0b
(posit16->real (real->posit16 (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)))
8.5b
(sqrt (posit16->real (real->posit16 (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))))
1.2b
(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
12×add-sqr-sqrt pow1
9×*-un-lft-identity add-cube-cbrt
6×add-cbrt-cube add-exp-log
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×swap-sqr associate-*r* associate-*l* sqrt-prod
1×pow2 rem-sqrt-square sqrt-pow1 pow-plus pow1/2 pow-prod-down prod-exp pow-sqr *-commutative pow-prod-up cbrt-unprod fma-udef sqr-sin remove-posit16 sin-mult unswap-sqr
Counts
4 → 68
Calls
4 calls:
Slowest
21.0ms
(* (sin kx) (sin kx))
1.0ms
(sqrt (posit16->real (real->posit16 (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))))
0.0ms
(posit16->real (real->posit16 (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)

series722.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
319.0ms
(sqrt (posit16->real (real->posit16 (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))))
216.0ms
(posit16->real (real->posit16 (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)))
163.0ms
(fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)
24.0ms
(* (sin kx) (sin kx))

simplify4.2s

Counts
41 → 80
Calls
41 calls:
Slowest
431.0ms
(* (sqrt (+ (* 4 (pow (sin ky) 2)) (* 4 (pow (sin kx) 2)))) (/ l Om))
420.0ms
(* (/ (* l 2) Om) (/ (* l 2) Om))
391.0ms
(* (sqrt (+ (* 4 (pow (sin ky) 2)) (* 4 (pow (sin kx) 2)))) (/ l Om))
370.0ms
(sqrt (sqrt (posit16->real (real->posit16 (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)))))
362.0ms
(sqrt (* (cbrt (posit16->real (real->posit16 (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)))) (cbrt (posit16->real (real->posit16 (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))))))

prune2.4s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.3b

localize99.0ms

Local error

Found 4 expressions with local error:

13.0b
(posit16->real (real->posit16 (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)))
13.0b
(posit16->real (real->posit16 (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)))
13.0b
(posit16->real (real->posit16 (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)))
8.5b
(sqrt (posit16->real (real->posit16 (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))))

rewrite4.0ms

Algorithm
rewrite-expression-head
Rules
6×add-sqr-sqrt
5×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×sqrt-prod remove-posit16
1×rem-sqrt-square sqrt-pow1 pow1/2
Counts
4 → 49
Calls
4 calls:
Slowest
2.0ms
(sqrt (posit16->real (real->posit16 (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))))
1.0ms
(posit16->real (real->posit16 (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)))
0.0ms
(posit16->real (real->posit16 (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)))
0.0ms
(posit16->real (real->posit16 (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)))

series911.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
336.0ms
(sqrt (posit16->real (real->posit16 (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))))
199.0ms
(posit16->real (real->posit16 (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)))
190.0ms
(posit16->real (real->posit16 (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)))
186.0ms
(posit16->real (real->posit16 (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)))

simplify5.2s

Counts
20 → 61
Calls
20 calls:
Slowest
562.0ms
(+ (* 4 (/ (* (pow l 2) (pow (sin ky) 2)) (pow Om 2))) (+ (* 4 (/ (* (pow (sin kx) 2) (pow l 2)) (pow Om 2))) 1))
479.0ms
(* (/ (* l 2) Om) (/ (* l 2) Om))
449.0ms
(* (/ (* l 2) Om) (/ (* l 2) Om))
436.0ms
(* (/ (* l 2) Om) (/ (* l 2) Om))
406.0ms
(sqrt (* (cbrt (posit16->real (real->posit16 (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)))) (cbrt (posit16->real (real->posit16 (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))))))

prune2.4s

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0.3b

regimes520.0ms

Accuracy

0% (0.8b remaining)

Error of 1.6b against oracle of 0.8b and baseline of 1.6b

bsearch7.0ms

end0.0ms

sample3.8s

Algorithm
intervals
Results
3.5s7999×body80valid
1.0ms1×body160valid