Details

Time bar (total: 4.5s)

sample33.0ms

Algorithm
intervals
Results
23.0ms275×body80valid

simplify5.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0177
1217
2217

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.9b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* y.re y.re) (* y.im y.im))
0.2b
(+ (* x.re y.re) (* x.im y.im))
26.5b
(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
9×times-frac
7×add-log-exp
5×add-exp-log add-cbrt-cube
4×flip3-+ flip-+
3×pow1 expm1-log1p-u associate-/r* log1p-expm1-u associate-/l*
2×+-commutative fma-def sum-log associate-/r/ associate-/l/
1×cbrt-undiv frac-2neg div-exp clear-num div-inv
Counts
3 → 61
Calls
3 calls:
2.0ms
(+ (* y.re y.re) (* y.im y.im))
2.0ms
(+ (* x.re y.re) (* x.im y.im))
10.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

series138.0ms

Counts
3 → 9
Calls
3 calls:
30.0ms
(+ (* y.re y.re) (* y.im y.im))
29.0ms
(+ (* x.re y.re) (* x.im y.im))
78.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify134.0ms

Algorithm
egg-herbie
Counts
70 → 70
Iterations

Useful iterations: 2 (30.0ms)

IterNodesCost
0290532
11199475
24872462
35001462

prune212.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 17.9b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1 (* (hypot y.re y.im) 1))
0.0b
(fma x.re y.re (* x.im y.im))
0.2b
(* (/ 1 (* (hypot y.re y.im) 1)) (/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1)))
17.5b
(/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1))

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
170×add-exp-log
92×prod-exp
63×div-exp
50×add-cbrt-cube
41×1-exp
17×cbrt-unprod
16×cbrt-undiv
15×rec-exp
14×add-sqr-sqrt
12×add-cube-cbrt *-un-lft-identity times-frac
9×pow1
7×associate-*r* associate-*l*
6×associate-/l*
4×expm1-log1p-u log1p-expm1-u div-inv add-log-exp
2×pow-flip frac-2neg pow-prod-down clear-num associate-/r*
1×frac-times associate-*r/ associate-*l/ *-commutative fma-udef inv-pow unswap-sqr
Counts
4 → 145
Calls
4 calls:
4.0ms
(/ 1 (* (hypot y.re y.im) 1))
0.0ms
(fma x.re y.re (* x.im y.im))
20.0ms
(* (/ 1 (* (hypot y.re y.im) 1)) (/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1)))
3.0ms
(/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1))

series402.0ms

Counts
4 → 12
Calls
4 calls:
56.0ms
(/ 1 (* (hypot y.re y.im) 1))
56.0ms
(fma x.re y.re (* x.im y.im))
178.0ms
(* (/ 1 (* (hypot y.re y.im) 1)) (/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1)))
112.0ms
(/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1))

simplify47.0ms

Algorithm
egg-herbie
Counts
157 → 157
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
04861191
11654892
25002884

prune294.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.7b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b
(hypot y.re y.im)
0.0b
(fma x.re y.re (* x.im y.im))
0.1b
(/ (/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im)) (* (hypot y.re y.im) 1))
17.5b
(/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im))

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
40×times-frac
26×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
23×add-exp-log
18×add-cbrt-cube
16×associate-/l*
10×div-exp
7×cbrt-undiv
4×pow1 expm1-log1p-u prod-exp associate-/r* log1p-expm1-u div-inv add-log-exp
2×frac-2neg 1-exp clear-num cbrt-unprod
1×hypot-udef fma-udef associate-/l/
Counts
4 → 99
Calls
4 calls:
0.0ms
(hypot y.re y.im)
0.0ms
(fma x.re y.re (* x.im y.im))
6.0ms
(/ (/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im)) (* (hypot y.re y.im) 1))
2.0ms
(/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im))

series322.0ms

Counts
4 → 12
Calls
4 calls:
50.0ms
(hypot y.re y.im)
38.0ms
(fma x.re y.re (* x.im y.im))
119.0ms
(/ (/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im)) (* (hypot y.re y.im) 1))
114.0ms
(/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im))

simplify80.0ms

Algorithm
egg-herbie
Counts
111 → 111
Iterations

Useful iterations: 3 (70.0ms)

IterNodesCost
0308794
11149701
23275701
35001693

prune509.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.6b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma x.re y.re (* x.im y.im))
0.1b
(/ (/ 1 (/ (hypot y.re y.im) (fma x.re y.re (* x.im y.im)))) (* (hypot y.re y.im) 1))
0.2b
(/ 1 (/ (hypot y.re y.im) (fma x.re y.re (* x.im y.im))))
17.5b
(/ (hypot y.re y.im) (fma x.re y.re (* x.im y.im)))

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
260×times-frac
124×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
81×add-exp-log
50×div-exp associate-/l*
32×add-cbrt-cube
17×associate-/r*
16×cbrt-undiv
15×1-exp div-inv
14×prod-exp
8×rec-exp
5×pow1
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×frac-2neg clear-num associate-/r/ cbrt-unprod
1×pow-flip fma-udef associate-/l/ inv-pow
Counts
4 → 246
Calls
4 calls:
0.0ms
(fma x.re y.re (* x.im y.im))
15.0ms
(/ (/ 1 (/ (hypot y.re y.im) (fma x.re y.re (* x.im y.im)))) (* (hypot y.re y.im) 1))
5.0ms
(/ 1 (/ (hypot y.re y.im) (fma x.re y.re (* x.im y.im))))
2.0ms
(/ (hypot y.re y.im) (fma x.re y.re (* x.im y.im)))

series424.0ms

Counts
4 → 12
Calls
4 calls:
40.0ms
(fma x.re y.re (* x.im y.im))
180.0ms
(/ (/ 1 (/ (hypot y.re y.im) (fma x.re y.re (* x.im y.im)))) (* (hypot y.re y.im) 1))
112.0ms
(/ 1 (/ (hypot y.re y.im) (fma x.re y.re (* x.im y.im))))
91.0ms
(/ (hypot y.re y.im) (fma x.re y.re (* x.im y.im)))

simplify85.0ms

Algorithm
egg-herbie
Counts
258 → 258
Iterations

Useful iterations: 2 (59.0ms)

IterNodesCost
07952590
136872260
250012098

prune484.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.6b

regimes176.0ms

Accuracy

38.5% (6.8b remaining)

Error of 12.2b against oracle of 5.5b and baseline of 16.5b

bsearch73.0ms

Steps
ItersRangePoint
8
3.938121820157591e+142
6.559931041703192e+145
9.012016494007182e+142
5
-2.0487505030059975e+136
-9.39907926608248e+135
-1.3620016266644103e+136

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02815
13115
23115

end0.0ms

sample902.0ms

Algorithm
intervals
Results
678.0ms8450×body80valid