Details

Time bar (total: 42.8s)

sample549.0ms

Algorithm
intervals
Results
267.0ms100×body1280valid
135.0ms60×body640valid
26.0ms21×body320valid
19.0ms60×body80valid
10.0ms15×body160valid

simplify1.3s

Counts
1 → 1

prune26.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 8.7b

localize32.0ms

Local error

Found 3 expressions with local error:

0.2b
(* (sin th) (/ (sin ky) (hypot (sin ky) (sin kx))))
0.2b
(/ (sin ky) (hypot (sin ky) (sin kx)))
0.1b
(hypot (sin ky) (sin kx))

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
24×add-sqr-sqrt
19×*-un-lft-identity times-frac add-cube-cbrt
13×associate-*r*
10×add-cbrt-cube add-exp-log
5×pow1
3×expm1-log1p-u associate-/r* associate-*l* insert-posit16 log1p-expm1-u associate-/l* add-log-exp
2×cbrt-undiv div-exp prod-exp cbrt-unprod div-inv unswap-sqr
1×hypot-udef clear-num frac-2neg pow-prod-down associate-*r/ *-commutative
Counts
3 → 76
Calls
3 calls:
Slowest
22.0ms
(* (sin th) (/ (sin ky) (hypot (sin ky) (sin kx))))
8.0ms
(/ (sin ky) (hypot (sin ky) (sin kx)))
0.0ms
(hypot (sin ky) (sin kx))

series775.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
343.0ms
(* (sin th) (/ (sin ky) (hypot (sin ky) (sin kx))))
228.0ms
(/ (sin ky) (hypot (sin ky) (sin kx)))
203.0ms
(hypot (sin ky) (sin kx))

simplify1.3s

Counts
85 → 85

prune1.3s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 8.6b

localize31.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (hypot (sin ky) (sin kx)) (sin ky))
0.2b
(/ 1 (/ (hypot (sin ky) (sin kx)) (sin ky)))
0.2b
(* (sin th) (/ 1 (/ (hypot (sin ky) (sin kx)) (sin ky))))
0.1b
(hypot (sin ky) (sin kx))

rewrite50.0ms

Algorithm
rewrite-expression-head
Rules
156×times-frac
104×add-sqr-sqrt
92×*-un-lft-identity
90×add-cube-cbrt
44×associate-*r*
36×add-exp-log
20×add-cbrt-cube
16×associate-/r*
15×div-exp
10×div-inv
7×pow1 cbrt-undiv prod-exp
6×associate-/l*
5×unswap-sqr
4×expm1-log1p-u rec-exp 1-exp insert-posit16 log1p-expm1-u add-log-exp
3×associate-*l* cbrt-unprod
2×clear-num frac-2neg associate-/r/
1×hypot-udef pow-prod-down associate-*r/ un-div-inv *-commutative pow-flip inv-pow
Counts
4 → 196
Calls
4 calls:
Slowest
27.0ms
(* (sin th) (/ 1 (/ (hypot (sin ky) (sin kx)) (sin ky))))
15.0ms
(/ 1 (/ (hypot (sin ky) (sin kx)) (sin ky)))
5.0ms
(/ (hypot (sin ky) (sin kx)) (sin ky))
0.0ms
(hypot (sin ky) (sin kx))

series895.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
336.0ms
(* (sin th) (/ 1 (/ (hypot (sin ky) (sin kx)) (sin ky))))
233.0ms
(/ 1 (/ (hypot (sin ky) (sin kx)) (sin ky)))
173.0ms
(/ (hypot (sin ky) (sin kx)) (sin ky))
153.0ms
(hypot (sin ky) (sin kx))

simplify946.0ms

Counts
208 → 208

prune3.6s

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 8.6b

localize52.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (hypot (sin ky) (sin kx)))
0.2b
(/ (/ 1 (hypot (sin ky) (sin kx))) (/ 1 (sin ky)))
0.2b
(* (sin th) (/ (/ 1 (hypot (sin ky) (sin kx))) (/ 1 (sin ky))))
0.1b
(/ 1 (sin ky))

rewrite87.0ms

Algorithm
rewrite-expression-head
Rules
863×times-frac
435×add-sqr-sqrt
406×*-un-lft-identity
400×add-cube-cbrt
174×associate-*r*
110×add-exp-log
68×div-exp
58×div-inv
38×add-cbrt-cube
19×associate-/r* associate-/l*
18×cbrt-undiv rec-exp 1-exp
17×prod-exp
10×unswap-sqr
8×pow1
5×cbrt-unprod
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×clear-num frac-2neg associate-*l*
2×associate-/r/ pow-flip inv-pow
1×pow-prod-down associate-*r/ *-commutative associate-/l/
Counts
4 → 520
Calls
4 calls:
Slowest
33.0ms
(* (sin th) (/ (/ 1 (hypot (sin ky) (sin kx))) (/ 1 (sin ky))))
11.0ms
(/ 1 (sin ky))
11.0ms
(/ (/ 1 (hypot (sin ky) (sin kx))) (/ 1 (sin ky)))
5.0ms
(/ 1 (hypot (sin ky) (sin kx)))

series1.3s

Counts
4 → 12
Calls
4 calls:
Slowest
649.0ms
(/ (/ 1 (hypot (sin ky) (sin kx))) (/ 1 (sin ky)))
400.0ms
(* (sin th) (/ (/ 1 (hypot (sin ky) (sin kx))) (/ 1 (sin ky))))
201.0ms
(/ 1 (hypot (sin ky) (sin kx)))
20.0ms
(/ 1 (sin ky))

simplify1.0s

Counts
532 → 532

prune9.2s

Pruning

20 alts after pruning (18 fresh and 2 done)

Merged error: 8.6b

localize46.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ (sin ky) (sqrt (hypot (sin ky) (sin kx))))
0.3b
(/ (sin th) (sqrt (hypot (sin ky) (sin kx))))
0.3b
(* (/ (sin th) (sqrt (hypot (sin ky) (sin kx)))) (/ (sin ky) (sqrt (hypot (sin ky) (sin kx)))))
0.1b
(sqrt (hypot (sin ky) (sin kx)))

rewrite47.0ms

Algorithm
rewrite-expression-head
Rules
92×add-sqr-sqrt
84×times-frac
61×*-un-lft-identity add-cube-cbrt
51×sqrt-prod
22×associate-*r* associate-*l*
20×add-cbrt-cube add-exp-log
12×associate-/r*
9×unswap-sqr
7×pow1
6×cbrt-undiv div-exp associate-/l*
4×expm1-log1p-u prod-exp cbrt-unprod insert-posit16 log1p-expm1-u div-inv add-log-exp
2×clear-num frac-2neg
1×frac-times rem-sqrt-square sqrt-pow1 pow1/2 pow-prod-down associate-*l/ associate-*r/ *-commutative
Counts
4 → 176
Calls
4 calls:
Slowest
23.0ms
(* (/ (sin th) (sqrt (hypot (sin ky) (sin kx)))) (/ (sin ky) (sqrt (hypot (sin ky) (sin kx)))))
11.0ms
(/ (sin ky) (sqrt (hypot (sin ky) (sin kx))))
8.0ms
(/ (sin th) (sqrt (hypot (sin ky) (sin kx))))
1.0ms
(sqrt (hypot (sin ky) (sin kx)))

series1.2s

Counts
4 → 12
Calls
4 calls:
Slowest
348.0ms
(* (/ (sin th) (sqrt (hypot (sin ky) (sin kx)))) (/ (sin ky) (sqrt (hypot (sin ky) (sin kx)))))
344.0ms
(/ (sin th) (sqrt (hypot (sin ky) (sin kx))))
297.0ms
(/ (sin ky) (sqrt (hypot (sin ky) (sin kx))))
193.0ms
(sqrt (hypot (sin ky) (sin kx)))

simplify931.0ms

Counts
188 → 188

prune3.2s

Pruning

21 alts after pruning (18 fresh and 3 done)

Merged error: 8.6b

regimes1.8s

Accuracy

0% (0.2b remaining)

Error of 8.6b against oracle of 8.4b and baseline of 8.6b

bsearch5.0ms

end0.0ms

sample13.2s

Algorithm
intervals
Results
7.6s2801×body1280valid
3.0s1795×body640valid
1.2s748×body320valid
854.0ms2310×body80valid
220.0ms346×body160valid