Details

Time bar (total: 4.1s)

sample22.0ms

Algorithm
intervals
Results
9.0ms272×body80valid

simplify10.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0197
1367
2487
3667
4727
5727
done727

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.4b

localize13.0ms

Local error

Found 2 expressions with local error:

1.2b
(- (* x.im y.re) (* x.re y.im))
26.8b
(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite34.0ms

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:
8.0ms
(- (* x.im y.re) (* x.re y.im))
25.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

series132.0ms

Counts
2 → 6
Calls
2 calls:
39.0ms
(- (* x.im y.re) (* x.re y.im))
93.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify101.0ms

Counts
50 → 50
Iterations

Useful iterations: 2 (24.0ms)

IterNodesCost
0251464
1938427
23504426
35001426
done5001426

prune135.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 26.6b

localize12.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (* x.im y.re) (* x.re y.im))
16.0b
(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
30.6b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
30.6b
(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite55.0ms

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:
7.0ms
(- (* x.im y.re) (* x.re y.im))
26.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
11.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
8.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

series236.0ms

Counts
4 → 12
Calls
4 calls:
39.0ms
(- (* x.im y.re) (* x.re y.im))
122.0ms
(/ (- (* 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)))
39.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify99.0ms

Counts
98 → 98
Iterations

Useful iterations: 2 (25.0ms)

IterNodesCost
0304912
1990857
23354845
35001845
done5001845

prune272.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 24.1b

localize19.0ms

Local error

Found 4 expressions with local error:

10.3b
(* (/ 1 (* (fabs (cbrt (+ (* y.re y.re) (* y.im y.im)))) 1)) (/ (- (* x.im y.re) (* x.re y.im)) (sqrt (cbrt (+ (* y.re y.re) (* y.im y.im))))))
30.6b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
31.7b
(cbrt (+ (* y.re y.re) (* y.im y.im)))
31.7b
(cbrt (+ (* y.re y.re) (* y.im y.im)))

rewrite103.0ms

Algorithm
rewrite-expression-head
Rules
66×add-exp-log
40×add-sqr-sqrt
33×times-frac associate-*r*
32×prod-exp
28×add-cube-cbrt *-un-lft-identity
25×add-cbrt-cube
23×sqrt-prod
22×div-exp
16×cbrt-prod
12×1-exp
8×cbrt-unprod
7×pow1 cbrt-undiv associate-*l*
6×rec-exp cbrt-div
4×flip3-+ sqrt-div flip-+ add-log-exp unswap-sqr
2×pow1/3 associate-/r/ div-inv
1×frac-times rem-sqrt-square sqrt-pow1 pow1/2 associate-*r/ pow-prod-down associate-*l/ *-commutative
Counts
4 → 123
Calls
4 calls:
80.0ms
(* (/ 1 (* (fabs (cbrt (+ (* y.re y.re) (* y.im y.im)))) 1)) (/ (- (* x.im y.re) (* x.re y.im)) (sqrt (cbrt (+ (* y.re y.re) (* y.im y.im))))))
8.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
5.0ms
(cbrt (+ (* y.re y.re) (* y.im y.im)))
5.0ms
(cbrt (+ (* y.re y.re) (* y.im y.im)))

series903.0ms

Counts
4 → 12
Calls
4 calls:
471.0ms
(* (/ 1 (* (fabs (cbrt (+ (* y.re y.re) (* y.im y.im)))) 1)) (/ (- (* x.im y.re) (* x.re y.im)) (sqrt (cbrt (+ (* y.re y.re) (* y.im y.im))))))
241.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
97.0ms
(cbrt (+ (* y.re y.re) (* y.im y.im)))
95.0ms
(cbrt (+ (* y.re y.re) (* y.im y.im)))

simplify79.0ms

Counts
135 → 135
Iterations

Useful iterations: 2 (63.0ms)

IterNodesCost
07492099
133631804
250021787
done50021787

prune453.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 24.1b

localize24.0ms

Local error

Found 4 expressions with local error:

30.6b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
30.6b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
30.6b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
31.7b
(cbrt (+ (* y.re y.re) (* y.im y.im)))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
9×sqrt-prod
8×add-cube-cbrt *-un-lft-identity
7×pow1
6×sqrt-div
4×add-exp-log flip3-+ add-cbrt-cube flip-+ add-log-exp
3×cbrt-prod rem-sqrt-square sqrt-pow1 pow1/2
2×cbrt-div
1×pow1/3
Counts
4 → 58
Calls
4 calls:
7.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
8.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
7.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
5.0ms
(cbrt (+ (* y.re y.re) (* y.im y.im)))

series209.0ms

Counts
4 → 12
Calls
4 calls:
38.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
36.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
40.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
95.0ms
(cbrt (+ (* y.re y.re) (* y.im y.im)))

simplify53.0ms

Counts
70 → 70
Iterations

Useful iterations: 3 (48.0ms)

IterNodesCost
0141422
1440404
21471402
35001399
done5001399

prune331.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 24.1b

regimes190.0ms

Accuracy

23% (2.2b remaining)

Error of 25.5b against oracle of 23.3b and baseline of 26.1b

bsearch2.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02526
12726
22726
done2726

end0.0ms

sample584.0ms

Algorithm
intervals
Results
295.0ms8516×body80valid