Details

Time bar (total: 3.7s)

sample21.0ms

Algorithm
intervals
Results
10.0ms268×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: 23.4b

localize13.0ms

Local error

Found 2 expressions with local error:

0.2b
(+ (* x.re y.re) (* x.im y.im))
23.0b
(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite13.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
9×times-frac
4×add-exp-log add-cbrt-cube add-log-exp
3×flip3-+ associate-/r* flip-+ associate-/l*
2×pow1 expm1-log1p-u associate-/r/ log1p-expm1-u associate-/l/
1×cbrt-undiv +-commutative fma-def frac-2neg div-exp clear-num sum-log div-inv
Counts
2 → 47
Calls
2 calls:
3.0ms
(+ (* x.re y.re) (* x.im y.im))
8.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

series108.0ms

Counts
2 → 6
Calls
2 calls:
29.0ms
(+ (* x.re y.re) (* x.im y.im))
79.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify89.0ms

Algorithm
egg-herbie
Counts
53 → 53
Iterations

Useful iterations: 2 (25.0ms)

IterNodesCost
0244458
1872411
23164403
35001403

prune169.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 14.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma x.re y.re (* x.im y.im))
0.0b
(/ 1 (* (hypot y.re y.im) 1))
0.2b
(* (/ 1 (* (hypot y.re y.im) 1)) (/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1)))
13.6b
(/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1))

rewrite28.0ms

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:
1.0ms
(fma x.re y.re (* x.im y.im))
5.0ms
(/ 1 (* (hypot y.re y.im) 1))
12.0ms
(* (/ 1 (* (hypot y.re y.im) 1)) (/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1)))
5.0ms
(/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1))

series399.0ms

Counts
4 → 12
Calls
4 calls:
42.0ms
(fma x.re y.re (* x.im y.im))
50.0ms
(/ 1 (* (hypot y.re y.im) 1))
184.0ms
(* (/ 1 (* (hypot y.re y.im) 1)) (/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1)))
122.0ms
(/ (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 (34.0ms)

IterNodesCost
04861191
11654892
25002884

prune496.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.8b

localize10.0ms

Local error

Found 3 expressions with local error:

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))
13.6b
(/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im))

rewrite13.0ms

Algorithm
rewrite-expression-head
Rules
40×times-frac
25×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
22×add-exp-log
17×add-cbrt-cube
16×associate-/l*
10×div-exp
7×cbrt-undiv
4×prod-exp associate-/r* div-inv
3×pow1 expm1-log1p-u log1p-expm1-u add-log-exp
2×frac-2neg 1-exp clear-num cbrt-unprod
1×fma-udef associate-/l/
Counts
3 → 89
Calls
3 calls:
1.0ms
(fma x.re y.re (* x.im y.im))
7.0ms
(/ (/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im)) (* (hypot y.re y.im) 1))
3.0ms
(/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im))

series258.0ms

Counts
3 → 9
Calls
3 calls:
36.0ms
(fma x.re y.re (* x.im y.im))
109.0ms
(/ (/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im)) (* (hypot y.re y.im) 1))
113.0ms
(/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im))

simplify82.0ms

Algorithm
egg-herbie
Counts
98 → 98
Iterations

Useful iterations: 3 (72.0ms)

IterNodesCost
0297767
11133677
23251677
35001670

prune280.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 6.8b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1 (hypot y.re y.im))
0.0b
(/ 1 (* (hypot y.re y.im) 1))
0.2b
(* (/ 1 (* (hypot y.re y.im) 1)) (* (/ 1 (hypot y.re y.im)) (fma x.re y.re (* x.im y.im))))
13.7b
(* (/ 1 (hypot y.re y.im)) (fma x.re y.re (* x.im y.im)))

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
212×add-exp-log
130×prod-exp
60×div-exp
52×add-cbrt-cube
48×1-exp
31×add-sqr-sqrt
30×rec-exp
26×times-frac
25×*-un-lft-identity
24×add-cube-cbrt
21×cbrt-unprod
20×associate-*l*
15×pow1
13×cbrt-undiv
6×fma-udef associate-/l*
5×distribute-rgt-in distribute-lft-in pow-prod-down
4×expm1-log1p-u associate-*r* associate-*l/ associate-/r* log1p-expm1-u div-inv add-log-exp
3×pow-flip unswap-sqr
2×frac-2neg clear-num *-commutative inv-pow
1×frac-times associate-*r/
Counts
4 → 191
Calls
4 calls:
3.0ms
(/ 1 (hypot y.re y.im))
5.0ms
(/ 1 (* (hypot y.re y.im) 1))
12.0ms
(* (/ 1 (* (hypot y.re y.im) 1)) (* (/ 1 (hypot y.re y.im)) (fma x.re y.re (* x.im y.im))))
9.0ms
(* (/ 1 (hypot y.re y.im)) (fma x.re y.re (* x.im y.im)))

series394.0ms

Counts
4 → 12
Calls
4 calls:
54.0ms
(/ 1 (hypot y.re y.im))
53.0ms
(/ 1 (* (hypot y.re y.im) 1))
176.0ms
(* (/ 1 (* (hypot y.re y.im) 1)) (* (/ 1 (hypot y.re y.im)) (fma x.re y.re (* x.im y.im))))
111.0ms
(* (/ 1 (hypot y.re y.im)) (fma x.re y.re (* x.im y.im)))

simplify57.0ms

Algorithm
egg-herbie
Counts
203 → 203
Iterations

Useful iterations: 2 (42.0ms)

IterNodesCost
06751500
123091125
250011046

prune322.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 5.4b

regimes180.0ms

Accuracy

35% (8.2b remaining)

Error of 12.8b against oracle of 4.6b and baseline of 17.2b

bsearch130.0ms

Steps
ItersRangePoint
10
1.464110213656478e+115
6.0573437940032564e+125
2.2413672752256256e+125
9
-3.9788200308749486e+18
-5288626288997.5625
-86223460658051.5
9
-1.2571754799481663e+163
-4.544732995620792e+155
-2.945998009177675e+158

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04227
14527
24527

end0.0ms

sample523.0ms

Algorithm
intervals
Results
308.0ms8456×body80valid