Details

Time bar (total: 8.4s)

sample53.0ms

Algorithm
intervals
Results
36.0ms267×body80valid

simplify70.0ms

Counts
1 → 1
Iterations
IterNodes
done70
570
466
348
236
119
011

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.1b

localize23.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* y.re y.re) (* y.im y.im))
0.5b
(- (* x.im y.re) (* x.re y.im))
24.1b
(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite59.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
9×times-frac
7×add-log-exp
5×add-cbrt-cube add-exp-log
3×pow1 associate-/r* insert-posit16 associate-/l*
2×flip3-+ flip3-- associate-/r/ flip-+ flip-- associate-/l/
1×cbrt-undiv +-commutative clear-num sum-log sub-neg frac-2neg diff-log div-sub div-exp div-inv
Counts
3 → 58
Calls
3 calls:
15.0ms
(+ (* y.re y.re) (* y.im y.im))
14.0ms
(- (* x.im y.re) (* x.re y.im))
29.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

series186.0ms

Counts
3 → 9
Calls
3 calls:
35.0ms
(+ (* y.re y.re) (* y.im y.im))
49.0ms
(- (* x.im y.re) (* x.re y.im))
101.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify616.0ms

Counts
67 → 67
Iterations
IterNodes
done2001
21186
1305
0104

prune320.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 23.6b

localize24.0ms

Local error

Found 4 expressions with local error:

0.5b
(- (* x.im y.re) (* x.re y.im))
15.9b
(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
31.0b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
31.0b
(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite45.0ms

Algorithm
rewrite-expression-head
Rules
23×add-sqr-sqrt
21×*-un-lft-identity add-cube-cbrt
18×times-frac sqrt-prod
6×pow1 associate-/r* add-cbrt-cube sqrt-div add-exp-log add-log-exp
4×insert-posit16
3×flip3-+ flip-+ associate-/l*
2×rem-sqrt-square sqrt-pow1 flip3-- pow1/2 associate-/r/ flip-- associate-/l/
1×cbrt-undiv clear-num sub-neg frac-2neg diff-log div-sub div-exp div-inv
Counts
4 → 90
Calls
4 calls:
7.0ms
(- (* x.im y.re) (* x.re y.im))
24.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
6.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
6.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

series297.0ms

Counts
4 → 12
Calls
4 calls:
59.0ms
(- (* x.im y.re) (* x.re y.im))
139.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
42.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
57.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify576.0ms

Counts
102 → 102
Iterations
IterNodes
done2000
2934
1315
0124

prune489.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 22.4b

localize32.0ms

Local error

Found 4 expressions with local error:

0.5b
(- (* x.im y.re) (* x.re y.im))
16.0b
(/ (sqrt (+ (* y.re y.re) (* y.im y.im))) (- (* x.im y.re) (* x.re y.im)))
31.0b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
31.0b
(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite43.0ms

Algorithm
rewrite-expression-head
Rules
23×add-sqr-sqrt
21×*-un-lft-identity add-cube-cbrt
18×times-frac sqrt-prod
6×pow1 add-cbrt-cube sqrt-div add-exp-log associate-/l* add-log-exp
4×insert-posit16
3×associate-/r* flip3-+ flip-+
2×rem-sqrt-square sqrt-pow1 flip3-- pow1/2 associate-/r/ flip-- associate-/l/
1×cbrt-undiv clear-num sub-neg frac-2neg diff-log div-exp div-inv
Counts
4 → 89
Calls
4 calls:
7.0ms
(- (* x.im y.re) (* x.re y.im))
23.0ms
(/ (sqrt (+ (* y.re y.re) (* y.im y.im))) (- (* x.im y.re) (* x.re y.im)))
6.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
6.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

series277.0ms

Counts
4 → 12
Calls
4 calls:
44.0ms
(- (* x.im y.re) (* x.re y.im))
117.0ms
(/ (sqrt (+ (* y.re y.re) (* y.im y.im))) (- (* x.im y.re) (* x.re y.im)))
64.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
51.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify569.0ms

Counts
101 → 101
Iterations
IterNodes
done2000
2759
1275
0119

prune527.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 22.4b

localize62.0ms

Local error

Found 4 expressions with local error:

8.2b
(* (/ 1 (sqrt (sqrt (+ (* y.re y.re) (* y.im y.im))))) (/ (- (* x.im y.re) (* x.re y.im)) (sqrt (sqrt (+ (* y.re y.re) (* y.im y.im))))))
31.0b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
31.0b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
31.0b
(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite87.0ms

Algorithm
rewrite-expression-head
Rules
137×add-sqr-sqrt
108×sqrt-prod
99×times-frac
57×*-un-lft-identity
45×add-cube-cbrt
33×associate-*r* associate-*l*
28×unswap-sqr
26×add-exp-log
16×add-cbrt-cube
14×sqrt-div
9×pow1
8×div-exp prod-exp
5×flip3-+ flip-+
4×cbrt-undiv associate-/r/ cbrt-unprod insert-posit16 add-log-exp
3×rem-sqrt-square sqrt-pow1 pow1/2
2×rec-exp 1-exp div-inv
1×frac-times pow-prod-down associate-*l/ associate-*r/ *-commutative
Counts
4 → 167
Calls
4 calls:
67.0ms
(* (/ 1 (sqrt (sqrt (+ (* y.re y.re) (* y.im y.im))))) (/ (- (* x.im y.re) (* x.re y.im)) (sqrt (sqrt (+ (* y.re y.re) (* y.im y.im))))))
6.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
6.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
6.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

series310.0ms

Counts
4 → 12
Calls
4 calls:
156.0ms
(* (/ 1 (sqrt (sqrt (+ (* y.re y.re) (* y.im y.im))))) (/ (- (* x.im y.re) (* x.re y.im)) (sqrt (sqrt (+ (* y.re y.re) (* y.im y.im))))))
57.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
49.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
47.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify976.0ms

Counts
179 → 179
Iterations
IterNodes
done2000
21797
1603
0201

prune847.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 22.4b

regimes535.0ms

Accuracy

0% (2.7b remaining)

Error of 25.9b against oracle of 23.2b and baseline of 25.9b

bsearch0.0ms

simplify2.0ms

Iterations
IterNodes
done20
120
015

end0.0ms

sample1.4s

Algorithm
intervals
Results
1.1s8493×body80valid