Details

Time bar (total: 13.1s)

sample51.0ms

Algorithm
intervals
Results
35.0ms263×body80valid

simplify10.0ms

Counts
1 → 1
Iterations
IterNodes
done21
221
117
011

prune14.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 27.3b

localize21.0ms

Local error

Found 3 expressions with local error:

0.0b
(fma y.im y.im (* y.re y.re))
0.0b
(fma x.re y.re (* x.im y.im))
27.3b
(/ (fma x.re y.re (* x.im y.im)) (fma y.im y.im (* y.re y.re)))

rewrite7.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
9×times-frac
5×add-cbrt-cube add-exp-log
3×expm1-log1p-u pow1 associate-/r* insert-posit16 log1p-expm1-u associate-/l* add-log-exp
2×fma-udef
1×cbrt-undiv clear-num frac-2neg div-exp div-inv
Counts
3 → 52
Calls
3 calls:
0.0ms
(fma y.im y.im (* y.re y.re))
0.0ms
(fma x.re y.re (* x.im y.im))
6.0ms
(/ (fma x.re y.re (* x.im y.im)) (fma y.im y.im (* y.re y.re)))

series217.0ms

Counts
3 → 9
Calls
3 calls:
41.0ms
(fma y.im y.im (* y.re y.re))
56.0ms
(fma x.re y.re (* x.im y.im))
121.0ms
(/ (fma x.re y.re (* x.im y.im)) (fma y.im y.im (* y.re y.re)))

simplify780.0ms

Counts
61 → 61
Iterations
IterNodes
done5001
31475
2357
1117
076

prune322.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 26.8b

localize35.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re)))) (sqrt (fma y.im y.im (* y.re y.re))))
18.4b
(/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
28.3b
(sqrt (fma y.im y.im (* y.re y.re)))
28.3b
(sqrt (fma y.im y.im (* y.re y.re)))

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
276×times-frac
160×add-sqr-sqrt
158×*-un-lft-identity add-cube-cbrt
150×sqrt-prod
25×associate-/l*
12×associate-/r*
11×add-cbrt-cube add-exp-log
9×div-inv
6×pow1
4×expm1-log1p-u cbrt-undiv div-exp insert-posit16 log1p-expm1-u add-log-exp
2×rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 fma-udef hypot-def
1×associate-/l/
Counts
4 → 254
Calls
4 calls:
14.0ms
(/ (/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re)))) (sqrt (fma y.im y.im (* y.re y.re))))
5.0ms
(/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
1.0ms
(sqrt (fma y.im y.im (* y.re y.re)))
2.0ms
(sqrt (fma y.im y.im (* y.re y.re)))

series360.0ms

Counts
4 → 12
Calls
4 calls:
114.0ms
(/ (/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re)))) (sqrt (fma y.im y.im (* y.re y.re))))
134.0ms
(/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
63.0ms
(sqrt (fma y.im y.im (* y.re y.re)))
49.0ms
(sqrt (fma y.im y.im (* y.re y.re)))

simplify1.2s

Counts
266 → 266
Iterations
IterNodes
done5001
22307
1568
0262

prune1.3s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 24.8b

localize38.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re)))) (/ 1 (sqrt (fma y.im y.im (* y.re y.re)))))
18.4b
(/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
28.3b
(sqrt (fma y.im y.im (* y.re y.re)))
28.3b
(sqrt (fma y.im y.im (* y.re y.re)))

rewrite48.0ms

Algorithm
rewrite-expression-head
Rules
95×add-sqr-sqrt
76×times-frac
53×*-un-lft-identity
47×add-cube-cbrt sqrt-prod
28×add-exp-log
22×associate-*r* associate-*l*
18×add-cbrt-cube
15×unswap-sqr
9×div-exp
8×pow1 prod-exp
6×associate-/r*
5×cbrt-undiv
4×expm1-log1p-u cbrt-unprod insert-posit16 log1p-expm1-u add-log-exp
3×div-inv associate-/l*
2×rem-sqrt-square rec-exp sqrt-pow1 pow1/2 1-exp fma-udef hypot-def
1×frac-times clear-num frac-2neg pow-prod-down associate-*l/ associate-*r/ un-div-inv *-commutative
Counts
4 → 163
Calls
4 calls:
27.0ms
(* (/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re)))) (/ 1 (sqrt (fma y.im y.im (* y.re y.re)))))
14.0ms
(/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
2.0ms
(sqrt (fma y.im y.im (* y.re y.re)))
2.0ms
(sqrt (fma y.im y.im (* y.re y.re)))

series382.0ms

Counts
4 → 12
Calls
4 calls:
99.0ms
(* (/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re)))) (/ 1 (sqrt (fma y.im y.im (* y.re y.re)))))
154.0ms
(/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
66.0ms
(sqrt (fma y.im y.im (* y.re y.re)))
63.0ms
(sqrt (fma y.im y.im (* y.re y.re)))

simplify3.9s

Counts
175 → 175
Iterations
IterNodes
done5001
23469
1468
0172

prune855.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 24.8b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma y.im y.im (* y.re y.re))
0.7b
(/ 1 (fma y.im y.im (* y.re y.re)))
0.8b
(fma x.im y.im (* y.re x.re))
26.7b
(* (fma x.im y.im (* y.re x.re)) (/ 1 (fma y.im y.im (* y.re y.re))))

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
27×add-sqr-sqrt
21×*-un-lft-identity
20×times-frac add-cube-cbrt
17×add-exp-log
13×associate-*r*
11×add-cbrt-cube
7×pow1
4×expm1-log1p-u div-exp prod-exp insert-posit16 log1p-expm1-u add-log-exp
3×associate-/r* associate-*l* associate-/l* unswap-sqr
2×cbrt-undiv rec-exp 1-exp cbrt-unprod fma-udef div-inv
1×clear-num frac-2neg pow-prod-down associate-*r/ un-div-inv *-commutative pow-flip inv-pow
Counts
4 → 95
Calls
4 calls:
0.0ms
(fma y.im y.im (* y.re y.re))
4.0ms
(/ 1 (fma y.im y.im (* y.re y.re)))
5.0ms
(fma x.im y.im (* y.re x.re))
10.0ms
(* (fma x.im y.im (* y.re x.re)) (/ 1 (fma y.im y.im (* y.re y.re))))

series282.0ms

Counts
4 → 12
Calls
4 calls:
36.0ms
(fma y.im y.im (* y.re y.re))
48.0ms
(/ 1 (fma y.im y.im (* y.re y.re)))
62.0ms
(fma x.im y.im (* y.re x.re))
136.0ms
(* (fma x.im y.im (* y.re x.re)) (/ 1 (fma y.im y.im (* y.re y.re))))

simplify1.0s

Counts
107 → 107
Iterations
IterNodes
done5002
21264
1226
0113

prune458.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 24.8b

regimes317.0ms

Accuracy

0% (3.0b remaining)

Error of 26.3b against oracle of 23.3b and baseline of 26.3b

bsearch0.0ms

simplify4.0ms

Iterations
IterNodes
done17
117
013

end0.0ms

sample1.5s

Algorithm
intervals
Results
1.2s8425×body80valid