Details

Time bar (total: 11.0s)

sample40.0ms

Algorithm
intervals
Results
26.0ms272×body80valid

simplify64.0ms

Counts
1 → 1
Iterations
IterNodes
670
570
466
348
236
119
011

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 23.7b

localize20.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* y.re y.re) (* y.im y.im))
1.1b
(- (* x.im y.re) (* x.re y.im))
23.7b
(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite62.0ms

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:
11.0ms
(+ (* y.re y.re) (* y.im y.im))
15.0ms
(- (* x.im y.re) (* x.re y.im))
35.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

series223.0ms

Counts
3 → 9
Calls
3 calls:
50.0ms
(+ (* y.re y.re) (* y.im y.im))
69.0ms
(- (* x.im y.re) (* x.re y.im))
104.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify1.5s

Counts
67 → 67
Iterations
IterNodes
34786
21199
1304
0104

prune357.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 23.3b

localize31.0ms

Local error

Found 4 expressions with local error:

1.1b
(- (* x.im y.re) (* x.re y.im))
13.7b
(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
28.2b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
28.2b
(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite59.0ms

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))
22.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
16.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
12.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

series313.0ms

Counts
4 → 12
Calls
4 calls:
59.0ms
(- (* x.im y.re) (* x.re y.im))
164.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
40.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
49.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify917.0ms

Counts
102 → 102
Iterations
IterNodes
32511
2896
1314
0124

prune617.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 21.5b

localize45.0ms

Local error

Found 4 expressions with local error:

7.8b
(* (/ 1 (fabs (cbrt (+ (* y.re y.re) (* y.im y.im))))) (/ (- (* x.im y.re) (* x.re y.im)) (sqrt (cbrt (+ (* y.re y.re) (* y.im y.im))))))
28.2b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
29.2b
(cbrt (+ (* y.re y.re) (* y.im y.im)))
29.2b
(cbrt (+ (* y.re y.re) (* y.im y.im)))

rewrite74.0ms

Algorithm
rewrite-expression-head
Rules
71×add-sqr-sqrt
53×times-frac
37×*-un-lft-identity
33×associate-*r* add-cube-cbrt
27×sqrt-prod
26×add-exp-log
18×cbrt-prod
16×add-cbrt-cube
13×associate-*l*
12×unswap-sqr
8×div-exp prod-exp
7×pow1
6×cbrt-div
4×cbrt-undiv flip3-+ sqrt-div cbrt-unprod flip-+ insert-posit16 add-log-exp
2×rec-exp pow1/3 1-exp associate-/r/ div-inv
1×frac-times rem-sqrt-square sqrt-pow1 pow1/2 pow-prod-down associate-*l/ associate-*r/ *-commutative
Counts
4 → 127
Calls
4 calls:
57.0ms
(* (/ 1 (fabs (cbrt (+ (* y.re y.re) (* y.im y.im))))) (/ (- (* x.im y.re) (* x.re y.im)) (sqrt (cbrt (+ (* y.re y.re) (* y.im y.im))))))
6.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
4.0ms
(cbrt (+ (* y.re y.re) (* y.im y.im)))
4.0ms
(cbrt (+ (* y.re y.re) (* y.im y.im)))

series753.0ms

Counts
4 → 12
Calls
4 calls:
484.0ms
(* (/ 1 (fabs (cbrt (+ (* y.re y.re) (* y.im y.im))))) (/ (- (* x.im y.re) (* x.re y.im)) (sqrt (cbrt (+ (* y.re y.re) (* y.im y.im))))))
54.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
118.0ms
(cbrt (+ (* y.re y.re) (* y.im y.im)))
96.0ms
(cbrt (+ (* y.re y.re) (* y.im y.im)))

simplify690.0ms

Counts
139 → 139
Iterations
IterNodes
22193
1719
0253

prune951.0ms

Pruning

13 alts after pruning (10 fresh and 3 done)

Merged error: 21.5b

localize46.0ms

Local error

Found 4 expressions with local error:

28.2b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
28.2b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
28.2b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
29.2b
(cbrt (+ (* y.re y.re) (* y.im y.im)))

rewrite36.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
9×sqrt-prod
8×*-un-lft-identity add-cube-cbrt
7×pow1
6×sqrt-div
4×flip3-+ add-cbrt-cube add-exp-log flip-+ insert-posit16 add-log-exp
3×cbrt-prod rem-sqrt-square sqrt-pow1 pow1/2
2×cbrt-div
1×pow1/3
Counts
4 → 62
Calls
4 calls:
10.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
8.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
12.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
4.0ms
(cbrt (+ (* y.re y.re) (* y.im y.im)))

series283.0ms

Counts
4 → 12
Calls
4 calls:
49.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
66.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
51.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
116.0ms
(cbrt (+ (* y.re y.re) (* y.im y.im)))

simplify932.0ms

Counts
74 → 74
Iterations
IterNodes
42612
3955
2339
1142
067

prune595.0ms

Pruning

13 alts after pruning (9 fresh and 4 done)

Merged error: 21.5b

regimes566.0ms

Accuracy

0% (2.6b remaining)

Error of 25.3b against oracle of 22.7b and baseline of 25.3b

bsearch0.0ms

simplify2.0ms

Iterations
IterNodes
216
116
013

end0.0ms

sample1.8s

Algorithm
intervals
Results
1.5s8454×body80valid