Details

Time bar (total: 4.3s)

sample19.0ms

Algorithm
intervals
Results
9.0ms269×body80valid

simplify6.0ms

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: 25.6b

localize9.0ms

Local error

Found 2 expressions with local error:

0.4b
(+ (* x.re y.re) (* x.im y.im))
25.2b
(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite14.0ms

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:
2.0ms
(+ (* 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)))

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)))

simplify87.0ms

Algorithm
egg-herbie
Counts
53 → 53
Iterations

Useful iterations: 2 (24.0ms)

IterNodesCost
0244458
1872411
23164403
35001403

prune164.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 15.0b

localize13.0ms

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))
0.3b
(* (/ 1 (* (hypot y.re y.im) 1)) (/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1)))
14.6b
(/ (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:
4.0ms
(/ 1 (* (hypot y.re y.im) 1))
0.0ms
(fma x.re y.re (* x.im y.im))
21.0ms
(* (/ 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:
50.0ms
(/ 1 (* (hypot y.re y.im) 1))
38.0ms
(fma x.re y.re (* x.im y.im))
176.0ms
(* (/ 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 (32.0ms)

IterNodesCost
04861191
11654892
25002884

prune273.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 6.0b

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))
14.6b
(/ (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))

series267.0ms

Counts
3 → 9
Calls
3 calls:
36.0ms
(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))
114.0ms
(/ (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

prune266.0ms

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 6.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma x.re y.re (* x.im y.im))
0.1b
(/ (hypot y.re y.im) (/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im)))
0.4b
(/ (/ 1 1) (/ (hypot y.re y.im) (/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im))))
14.6b
(/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im))

rewrite102.0ms

Algorithm
rewrite-expression-head
Rules
1985×times-frac
859×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
108×div-inv
71×add-exp-log
60×associate-/r*
58×div-exp
32×add-cbrt-cube
19×cbrt-undiv associate-/l*
16×associate-/r/
15×1-exp
6×rec-exp
4×pow1 expm1-log1p-u log1p-expm1-u add-log-exp
3×frac-2neg clear-num
1×fma-udef associate-/l/
Counts
4 → 781
Calls
4 calls:
0.0ms
(fma x.re y.re (* x.im y.im))
5.0ms
(/ (hypot y.re y.im) (/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im)))
26.0ms
(/ (/ 1 1) (/ (hypot y.re y.im) (/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im))))
2.0ms
(/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im))

series418.0ms

Counts
4 → 12
Calls
4 calls:
39.0ms
(fma x.re y.re (* x.im y.im))
86.0ms
(/ (hypot y.re y.im) (/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im)))
179.0ms
(/ (/ 1 1) (/ (hypot y.re y.im) (/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im))))
114.0ms
(/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im))

simplify171.0ms

Algorithm
egg-herbie
Counts
793 → 793
Iterations

Useful iterations: 1 (52.0ms)

IterNodesCost
0347813688
1500112813

prune1.1s

Pruning

15 alts after pruning (13 fresh and 2 done)

Merged error: 6.0b

regimes225.0ms

Accuracy

36.4% (7.2b remaining)

Error of 12.9b against oracle of 5.7b and baseline of 17.0b

bsearch59.0ms

Steps
ItersRangePoint
8
9.48819792626798e+151
4.839113402874256e+155
2.7202606860941377e+154
6
-7.857046442604841e+147
-1.2379330794402539e+147
-1.2881291875463798e+147

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02714
13014
23014

end0.0ms

sample497.0ms

Algorithm
intervals
Results
293.0ms8463×body80valid