Details

Time bar (total: 14.5s)

sample62.0ms

Algorithm
intervals
Results
41.0ms270×body80valid

simplify73.0ms

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

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.2b

localize44.0ms

Local error

Found 2 expressions with local error:

0.5b
(- (* x.im y.re) (* x.re y.im))
25.2b
(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
9×times-frac
4×add-cbrt-cube add-exp-log add-log-exp
3×associate-/r* associate-/l*
2×pow1 flip3-- associate-/r/ insert-posit16 flip-- associate-/l/
1×cbrt-undiv clear-num sub-neg frac-2neg flip3-+ diff-log div-sub div-exp flip-+ div-inv
Counts
2 → 46
Calls
2 calls:
10.0ms
(- (* x.im y.re) (* x.re y.im))
20.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

series167.0ms

Counts
2 → 6
Calls
2 calls:
56.0ms
(- (* x.im y.re) (* x.re y.im))
111.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify909.0ms

Counts
52 → 52
Iterations
IterNodes
32961
2897
1260
091

prune568.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 24.8b

localize29.0ms

Local error

Found 4 expressions with local error:

0.5b
(- (* x.im y.re) (* x.re y.im))
16.3b
(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
29.5b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
29.5b
(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite92.0ms

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:
15.0ms
(- (* x.im y.re) (* x.re y.im))
50.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
13.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
13.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

series304.0ms

Counts
4 → 12
Calls
4 calls:
62.0ms
(- (* x.im y.re) (* x.re y.im))
137.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
48.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
57.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify870.0ms

Counts
102 → 102
Iterations
IterNodes
32589
2934
1315
0124

prune1.3s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 23.2b

localize61.0ms

Local error

Found 4 expressions with local error:

9.3b
(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (sqrt (+ (* y.re y.re) (* y.im y.im)))))
29.5b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
29.5b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
29.5b
(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite86.0ms

Algorithm
rewrite-expression-head
Rules
45×sqrt-prod
32×add-sqr-sqrt
29×*-un-lft-identity add-cube-cbrt
27×times-frac
10×sqrt-div
9×associate-/r*
7×pow1
6×add-cbrt-cube add-exp-log
4×flip3-+ flip-+ insert-posit16 add-log-exp
3×rem-sqrt-square sqrt-pow1 pow1/2 associate-/l*
2×associate-/r/ associate-/l/
1×cbrt-undiv clear-num frac-2neg flip3-- div-sub div-exp div-inv flip--
Counts
4 → 105
Calls
4 calls:
51.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (sqrt (+ (* y.re y.re) (* y.im y.im)))))
11.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
10.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
10.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

series429.0ms

Counts
4 → 12
Calls
4 calls:
268.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (sqrt (+ (* y.re y.re) (* y.im y.im)))))
49.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
52.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
60.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify827.0ms

Counts
117 → 117
Iterations
IterNodes
32469
2911
1341
0147

prune1.8s

Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 23.2b

localize42.0ms

Local error

Found 4 expressions with local error:

9.5b
(* (/ 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))))))
29.5b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
30.6b
(cbrt (+ (* y.re y.re) (* y.im y.im)))
30.6b
(cbrt (+ (* y.re y.re) (* y.im y.im)))

rewrite68.0ms

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:
52.0ms
(* (/ 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)))

series903.0ms

Counts
4 → 12
Calls
4 calls:
604.0ms
(* (/ 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))))))
39.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
141.0ms
(cbrt (+ (* y.re y.re) (* y.im y.im)))
118.0ms
(cbrt (+ (* y.re y.re) (* y.im y.im)))

simplify867.0ms

Counts
139 → 139
Iterations
IterNodes
22217
1720
0253

prune2.3s

Pruning

14 alts after pruning (10 fresh and 4 done)

Merged error: 22.8b

regimes713.0ms

Accuracy

-9.7% (2.5b remaining)

Error of 25.9b against oracle of 23.4b and baseline of 25.7b

bsearch42.0ms

Steps
ItersRangePoint
5
5.461763845755053e+58
1.6053559124068705e+59
9.136570255790176e+58

simplify6.0ms

Iterations
IterNodes
223
123
018

end0.0ms

sample1.8s

Algorithm
intervals
Results
1.5s8496×body80valid