Details

Time bar (total: 3.7s)

sample20.0ms

Algorithm
intervals
Results
10.0ms272×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: 22.9b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* y.re y.re) (* y.im y.im))
0.3b
(+ (* x.re y.re) (* x.im y.im))
22.5b
(/ (+ (* 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)))

series135.0ms

Counts
3 → 9
Calls
3 calls:
28.0ms
(+ (* y.re y.re) (* y.im y.im))
29.0ms
(+ (* x.re y.re) (* x.im y.im))
77.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify135.0ms

Algorithm
egg-herbie
Counts
70 → 70
Iterations

Useful iterations: 2 (30.0ms)

IterNodesCost
0290532
11199475
24872462
35001462

prune205.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 15.1b

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)))
14.7b
(/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1))

rewrite34.0ms

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:
0.0ms
(fma x.re y.re (* x.im y.im))
4.0ms
(/ 1 (* (hypot y.re y.im) 1))
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))

series376.0ms

Counts
4 → 12
Calls
4 calls:
38.0ms
(fma x.re y.re (* x.im y.im))
49.0ms
(/ 1 (* (hypot y.re y.im) 1))
175.0ms
(* (/ 1 (* (hypot y.re y.im) 1)) (/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1)))
113.0ms
(/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1))

simplify46.0ms

Algorithm
egg-herbie
Counts
157 → 157
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
04861199
11655892
25001884

prune277.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 5.3b

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))
14.7b
(/ (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:
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))

series264.0ms

Counts
3 → 9
Calls
3 calls:
37.0ms
(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)) (* (hypot y.re y.im) 1))
112.0ms
(/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im))

simplify76.0ms

Algorithm
egg-herbie
Counts
98 → 98
Iterations

Useful iterations: 3 (68.0ms)

IterNodesCost
0297767
11133677
23251677
35001670

prune263.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.2b

localize11.0ms

Local error

Found 4 expressions with local error:

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)))))
0.3b
(/ 1 (/ (hypot y.re y.im) (fma x.re y.re (* x.im y.im))))
14.8b
(/ (hypot y.re y.im) (fma x.re y.re (* x.im y.im)))

rewrite62.0ms

Algorithm
rewrite-expression-head
Rules
264×add-exp-log
162×times-frac
126×div-exp
118×prod-exp
107×add-sqr-sqrt
95×*-un-lft-identity
93×add-cube-cbrt
70×1-exp
52×add-cbrt-cube
46×rec-exp
44×associate-*r*
21×cbrt-undiv
17×associate-/r*
15×pow1
13×cbrt-unprod
12×div-inv
9×associate-/l*
7×pow-flip associate-*l*
6×pow-prod-down
5×unswap-sqr
4×expm1-log1p-u log1p-expm1-u inv-pow add-log-exp
3×frac-2neg clear-num
2×associate-/r/
1×frac-times associate-*r/ associate-*l/ un-div-inv *-commutative
Counts
4 → 293
Calls
4 calls:
4.0ms
(/ 1 (* (hypot y.re y.im) 1))
36.0ms
(* (/ 1 (* (hypot y.re y.im) 1)) (/ 1 (/ (hypot y.re y.im) (fma x.re y.re (* x.im y.im)))))
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)))

series426.0ms

Counts
4 → 12
Calls
4 calls:
49.0ms
(/ 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)))))
110.0ms
(/ 1 (/ (hypot y.re y.im) (fma x.re y.re (* x.im y.im))))
90.0ms
(/ (hypot y.re y.im) (fma x.re y.re (* x.im y.im)))

simplify86.0ms

Algorithm
egg-herbie
Counts
305 → 305
Iterations

Useful iterations: 2 (57.0ms)

IterNodesCost
010242763
139452410
250012207

prune510.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 5.2b

regimes154.0ms

Accuracy

31.5% (7.8b remaining)

Error of 13.8b against oracle of 6.0b and baseline of 17.4b

bsearch75.0ms

Steps
ItersRangePoint
9
9.049284248076656e+175
8.048742643953444e+181
1.7187819587037017e+178
8
-4.2002350228108203e+76
-1.3647412722380514e+74
-4.153623860284757e+76

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02714
13014
23014

end0.0ms

sample510.0ms

Algorithm
intervals
Results
303.0ms8448×body80valid