Details

Time bar (total: 3.7s)

sample37.0ms

Algorithm
intervals
Results
26.0ms270×body80valid

simplify6.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0177
1217
2217

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.1b

localize10.0ms

Local error

Found 2 expressions with local error:

0.7b
(+ (* x.re y.re) (* x.im y.im))
27.6b
(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite15.0ms

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))
11.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

series112.0ms

Counts
2 → 6
Calls
2 calls:
31.0ms
(+ (* x.re y.re) (* x.im y.im))
82.0ms
(/ (+ (* 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

prune148.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 16.2b

localize13.0ms

Local error

Found 3 expressions with local error:

0.3b
(* (/ 1 (* (hypot y.re y.im) 1)) (/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1)))
0.5b
(fma x.re y.re (* x.im y.im))
15.9b
(/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1))

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
154×add-exp-log
86×prod-exp
57×div-exp
44×add-cbrt-cube
35×1-exp
16×cbrt-unprod
14×cbrt-undiv
12×rec-exp
11×add-sqr-sqrt
9×add-cube-cbrt *-un-lft-identity times-frac
7×associate-*r* associate-*l*
5×pow1
3×expm1-log1p-u log1p-expm1-u div-inv associate-/l* add-log-exp
1×frac-times frac-2neg associate-*r/ pow-prod-down associate-*l/ clear-num associate-/r* *-commutative fma-udef unswap-sqr
Counts
3 → 112
Calls
3 calls:
21.0ms
(* (/ 1 (* (hypot y.re y.im) 1)) (/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1)))
0.0ms
(fma x.re y.re (* x.im y.im))
3.0ms
(/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1))

series332.0ms

Counts
3 → 9
Calls
3 calls:
181.0ms
(* (/ 1 (* (hypot y.re y.im) 1)) (/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1)))
39.0ms
(fma x.re y.re (* x.im y.im))
112.0ms
(/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1))

simplify43.0ms

Algorithm
egg-herbie
Counts
121 → 121
Iterations

Useful iterations: 2 (33.0ms)

IterNodesCost
04721079
11607796
25001794

prune208.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.6b

localize10.0ms

Local error

Found 3 expressions with local error:

0.1b
(/ (/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im)) (* (hypot y.re y.im) 1))
0.5b
(fma x.re y.re (* x.im y.im))
15.9b
(/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im))

rewrite11.0ms

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:
6.0ms
(/ (/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im)) (* (hypot y.re y.im) 1))
0.0ms
(fma x.re y.re (* x.im y.im))
2.0ms
(/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im))

series274.0ms

Counts
3 → 9
Calls
3 calls:
116.0ms
(/ (/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im)) (* (hypot y.re y.im) 1))
42.0ms
(fma x.re y.re (* x.im y.im))
116.0ms
(/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im))

simplify77.0ms

Algorithm
egg-herbie
Counts
98 → 98
Iterations

Useful iterations: 3 (68.0ms)

IterNodesCost
0297767
11133677
23251677
35001670

prune256.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 5.5b

localize9.0ms

Local error

Found 3 expressions with local error:

0.3b
(* (/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im)) (/ 1 (hypot y.re y.im)))
0.5b
(fma x.re y.re (* x.im y.im))
15.9b
(/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im))

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
42×add-sqr-sqrt
34×times-frac
27×add-exp-log *-un-lft-identity
25×add-cube-cbrt
17×add-cbrt-cube
13×associate-*r* associate-*l*
9×div-exp
8×prod-exp
6×unswap-sqr
5×pow1 cbrt-undiv
4×cbrt-unprod
3×expm1-log1p-u associate-/r* log1p-expm1-u div-inv associate-/l* add-log-exp
2×rec-exp 1-exp
1×frac-times frac-2neg associate-*r/ pow-prod-down associate-*l/ clear-num un-div-inv *-commutative fma-udef
Counts
3 → 98
Calls
3 calls:
13.0ms
(* (/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im)) (/ 1 (hypot y.re y.im)))
0.0ms
(fma x.re y.re (* x.im y.im))
2.0ms
(/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im))

series269.0ms

Counts
3 → 9
Calls
3 calls:
117.0ms
(* (/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im)) (/ 1 (hypot y.re y.im)))
37.0ms
(fma x.re y.re (* x.im y.im))
115.0ms
(/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im))

simplify49.0ms

Algorithm
egg-herbie
Counts
107 → 107
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
0366859
11597749
25002737

prune254.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 5.5b

regimes243.0ms

Accuracy

38% (7.1b remaining)

Error of 12.8b against oracle of 5.7b and baseline of 17.1b

bsearch101.0ms

Steps
ItersRangePoint
8
1.108985634214693e+173
1.0860681284584067e+176
1.5555378499724725e+174
9
-3.5565145629661977e+171
-1.646701887901344e+164
-1.0042415763270424e+167

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02714
13014
23014

end0.0ms

sample1.0s

Algorithm
intervals
Results
819.0ms8533×body80valid