Details

Time bar (total: 17.6s)

sample57.0ms

Algorithm
intervals
Results
39.0ms280×body80valid

simplify17.0ms

Counts
1 → 1
Iterations
IterNodes
done21
221
117
011

prune27.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.9b

localize35.0ms

Local error

Found 2 expressions with local error:

0.0b
(fma y.im y.im (* y.re y.re))
24.9b
(/ (fma x.re y.re (* x.im y.im)) (fma y.im y.im (* y.re y.re)))

rewrite13.0ms

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
3×associate-/r* associate-/l*
2×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u add-log-exp
1×cbrt-undiv clear-num frac-2neg div-exp fma-udef div-inv
Counts
2 → 41
Calls
2 calls:
1.0ms
(fma y.im y.im (* y.re y.re))
11.0ms
(/ (fma x.re y.re (* x.im y.im)) (fma y.im y.im (* y.re y.re)))

series198.0ms

Counts
2 → 6
Calls
2 calls:
37.0ms
(fma y.im y.im (* y.re y.re))
161.0ms
(/ (fma x.re y.re (* x.im y.im)) (fma y.im y.im (* y.re y.re)))

simplify3.8s

Counts
47 → 47
Iterations
IterNodes
done5000
44956
3991
2277
1109
068

prune245.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 24.5b

localize24.0ms

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))))
15.0b
(/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
28.4b
(sqrt (fma y.im y.im (* y.re y.re)))
28.4b
(sqrt (fma y.im y.im (* y.re y.re)))

rewrite45.0ms

Algorithm
rewrite-expression-head
Rules
276×times-frac
163×add-sqr-sqrt
161×*-un-lft-identity add-cube-cbrt
153×sqrt-prod
28×associate-/l*
18×associate-/r*
12×associate-/l/
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
3×clear-num frac-2neg
2×rem-sqrt-square sqrt-pow1 pow1/2 fma-udef hypot-def
Counts
4 → 265
Calls
4 calls:
19.0ms
(/ (/ (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))))
6.0ms
(/ (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)))

series338.0ms

Counts
4 → 12
Calls
4 calls:
115.0ms
(/ (/ (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))))
124.0ms
(/ (fma x.re y.re (* x.im y.im)) (sqrt (fma y.im y.im (* y.re y.re))))
49.0ms
(sqrt (fma y.im y.im (* y.re y.re)))
50.0ms
(sqrt (fma y.im y.im (* y.re y.re)))

simplify2.3s

Counts
277 → 277
Iterations
IterNodes
done5229
34093
21189
1557
0269

prune1.6s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 14.2b

localize32.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (hypot y.im y.re) (/ (hypot y.im y.re) (fma x.im y.im (* y.re x.re))))
0.5b
(fma x.im y.im (* y.re x.re))
0.7b
(/ 1 (* (hypot y.im y.re) (/ (hypot y.im y.re) (fma x.im y.im (* y.re x.re)))))
15.1b
(/ (hypot y.im y.re) (fma x.im y.im (* y.re x.re)))

rewrite103.0ms

Algorithm
rewrite-expression-head
Rules
128×times-frac
109×add-sqr-sqrt
86×*-un-lft-identity
84×add-cube-cbrt
65×associate-*r*
32×associate-/r* add-exp-log
20×add-cbrt-cube
18×associate-*r/
15×associate-*l*
14×associate-/l*
11×div-exp associate-/r/
10×unswap-sqr
9×pow1
8×prod-exp
7×div-inv
6×cbrt-undiv clear-num
5×*-commutative
4×expm1-log1p-u frac-2neg un-div-inv cbrt-unprod insert-posit16 log1p-expm1-u add-log-exp
3×rec-exp 1-exp
2×pow-prod-down pow-flip
1×fma-udef inv-pow
Counts
4 → 220
Calls
4 calls:
27.0ms
(* (hypot y.im y.re) (/ (hypot y.im y.re) (fma x.im y.im (* y.re x.re))))
0.0ms
(fma x.im y.im (* y.re x.re))
56.0ms
(/ 1 (* (hypot y.im y.re) (/ (hypot y.im y.re) (fma x.im y.im (* y.re x.re)))))
8.0ms
(/ (hypot y.im y.re) (fma x.im y.im (* y.re x.re)))

series528.0ms

Counts
4 → 12
Calls
4 calls:
117.0ms
(* (hypot y.im y.re) (/ (hypot y.im y.re) (fma x.im y.im (* y.re x.re))))
44.0ms
(fma x.im y.im (* y.re x.re))
240.0ms
(/ 1 (* (hypot y.im y.re) (/ (hypot y.im y.re) (fma x.im y.im (* y.re x.re)))))
126.0ms
(/ (hypot y.im y.re) (fma x.im y.im (* y.re x.re)))

simplify1.8s

Counts
232 → 232
Iterations
IterNodes
done5000
21990
1676
0256

prune1.2s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 13.9b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(hypot y.im y.re)
0.1b
(/ (/ (fma y.im x.im (* y.re x.re)) (hypot y.im y.re)) (hypot y.im y.re))
0.5b
(fma y.im x.im (* y.re x.re))
15.0b
(/ (fma y.im x.im (* y.re x.re)) (hypot y.im y.re))

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
84×times-frac
56×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
19×associate-/l*
11×add-cbrt-cube add-exp-log
9×associate-/r* associate-/l/
6×div-inv
4×expm1-log1p-u pow1 cbrt-undiv div-exp insert-posit16 log1p-expm1-u add-log-exp
3×clear-num frac-2neg
1×hypot-udef fma-udef
Counts
4 → 133
Calls
4 calls:
5.0ms
(hypot y.im y.re)
13.0ms
(/ (/ (fma y.im x.im (* y.re x.re)) (hypot y.im y.re)) (hypot y.im y.re))
0.0ms
(fma y.im x.im (* y.re x.re))
5.0ms
(/ (fma y.im x.im (* y.re x.re)) (hypot y.im y.re))

series463.0ms

Counts
4 → 12
Calls
4 calls:
72.0ms
(hypot y.im y.re)
177.0ms
(/ (/ (fma y.im x.im (* y.re x.re)) (hypot y.im y.re)) (hypot y.im y.re))
61.0ms
(fma y.im x.im (* y.re x.re))
152.0ms
(/ (fma y.im x.im (* y.re x.re)) (hypot y.im y.re))

simplify2.2s

Counts
145 → 145
Iterations
IterNodes
done5107
33804
2982
1370
0176

prune723.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.0b

regimes339.0ms

Accuracy

36% (7.1b remaining)

Error of 11.9b against oracle of 4.8b and baseline of 16.0b

bsearch73.0ms

Steps
ItersRangePoint
5
1.1557624945669879e+141
2.8347486911993956e+141
2.2908775229370544e+141
8
-4.843369791675614e+163
-3.80336143295907e+160
-4.434994773334765e+162

simplify3.0ms

Iterations
IterNodes
done20
120
018

end0.0ms

sample1.5s

Algorithm
intervals
Results
1.2s8478×body80valid