Details

Time bar (total: 8.5s)

sample24.0ms

Algorithm
intervals
Results
13.0ms275×body80valid

simplify34.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01115
11915
23615
34815
46615
57215
done7215

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 22.6b

localize13.0ms

Local error

Found 2 expressions with local error:

0.3b
(- (* x.im y.re) (* x.re y.im))
22.3b
(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
9×times-frac
4×add-exp-log add-cbrt-cube add-log-exp
3×associate-/r* associate-/l*
2×pow1 flip3-- associate-/r/ flip-- associate-/l/
1×cbrt-undiv sub-neg frac-2neg flip3-+ diff-log div-sub div-exp clear-num flip-+ div-inv
Counts
2 → 44
Calls
2 calls:
2.0ms
(- (* x.im y.re) (* x.re y.im))
10.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

series125.0ms

Counts
2 → 6
Calls
2 calls:
36.0ms
(- (* x.im y.re) (* x.re y.im))
89.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify1.0s

Counts
50 → 50
Iterations

Useful iterations: done (1.0s)

IterNodesCost
089954
1250936
2854854
32891850
done5000849

prune143.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 21.9b

localize12.0ms

Local error

Found 4 expressions with local error:

0.3b
(- (* x.im y.re) (* x.re y.im))
12.0b
(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
28.1b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
28.1b
(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
23×add-sqr-sqrt
21×add-cube-cbrt *-un-lft-identity
18×times-frac sqrt-prod
6×pow1 add-exp-log sqrt-div associate-/r* add-cbrt-cube add-log-exp
3×flip3-+ flip-+ associate-/l*
2×rem-sqrt-square flip3-- sqrt-pow1 pow1/2 associate-/r/ flip-- associate-/l/
1×cbrt-undiv sub-neg frac-2neg diff-log div-sub div-exp clear-num div-inv
Counts
4 → 86
Calls
4 calls:
2.0ms
(- (* x.im y.re) (* x.re y.im))
14.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
3.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
4.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

series225.0ms

Counts
4 → 12
Calls
4 calls:
36.0ms
(- (* x.im y.re) (* x.re y.im))
119.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
35.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
36.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify1.0s

Counts
98 → 98
Iterations

Useful iterations: done (1.0s)

IterNodesCost
01211814
13111690
29271576
327831560
done50001559

prune310.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 20.9b

localize14.0ms

Local error

Found 4 expressions with local error:

0.3b
(- (* x.im y.re) (* x.re y.im))
12.1b
(/ (sqrt (+ (* y.re y.re) (* y.im y.im))) (- (* x.im y.re) (* x.re y.im)))
28.1b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
28.1b
(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
23×add-sqr-sqrt
21×add-cube-cbrt *-un-lft-identity
18×times-frac sqrt-prod
6×pow1 add-exp-log sqrt-div add-cbrt-cube associate-/l* add-log-exp
3×flip3-+ associate-/r* flip-+
2×rem-sqrt-square flip3-- sqrt-pow1 pow1/2 associate-/r/ flip-- associate-/l/
1×cbrt-undiv sub-neg frac-2neg diff-log div-exp clear-num div-inv
Counts
4 → 85
Calls
4 calls:
2.0ms
(- (* x.im y.re) (* x.re y.im))
10.0ms
(/ (sqrt (+ (* y.re y.re) (* y.im y.im))) (- (* x.im y.re) (* x.re y.im)))
3.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
4.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

series198.0ms

Counts
4 → 12
Calls
4 calls:
36.0ms
(- (* x.im y.re) (* x.re y.im))
84.0ms
(/ (sqrt (+ (* y.re y.re) (* y.im y.im))) (- (* x.im y.re) (* x.re y.im)))
41.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
36.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify760.0ms

Counts
97 → 97
Iterations

Useful iterations: done (756.0ms)

IterNodesCost
01161782
12711664
27551562
319421548
done50021547

prune306.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 20.9b

localize14.0ms

Local error

Found 4 expressions with local error:

0.3b
(- (* x.im y.re) (* x.re y.im))
12.1b
(* (- (* x.im y.re) (* x.re y.im)) (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im)))))
28.1b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
28.1b
(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite43.0ms

Algorithm
rewrite-expression-head
Rules
34×add-sqr-sqrt
24×associate-*r*
22×*-un-lft-identity times-frac
20×add-cube-cbrt
17×sqrt-prod
13×add-exp-log
9×add-cbrt-cube
8×pow1
6×sqrt-div add-log-exp
5×unswap-sqr
4×prod-exp
3×flip3-- flip3-+ associate-*l* flip-- flip-+
2×frac-times rem-sqrt-square sqrt-pow1 pow1/2 div-exp associate-*l/ associate-/r/ cbrt-unprod
1×cbrt-undiv sub-neg rec-exp diff-log 1-exp associate-*r/ pow-prod-down un-div-inv *-commutative div-inv
Counts
4 → 95
Calls
4 calls:
2.0ms
(- (* x.im y.re) (* x.re y.im))
29.0ms
(* (- (* x.im y.re) (* x.re y.im)) (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im)))))
4.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
4.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

series229.0ms

Counts
4 → 12
Calls
4 calls:
36.0ms
(- (* x.im y.re) (* x.re y.im))
115.0ms
(* (- (* x.im y.re) (* x.re y.im)) (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im)))))
41.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
36.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify2.9s

Counts
107 → 107
Iterations

Useful iterations: 3 (1.0s)

IterNodesCost
01481896
13921689
214001483
345221467
done50001467

prune294.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 20.9b

regimes192.0ms

Accuracy

0% (2.2b remaining)

Error of 25.9b against oracle of 23.8b and baseline of 25.9b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01527
12027
done2027

end0.0ms

sample517.0ms

Algorithm
intervals
Results
305.0ms8478×body80valid