Details

Time bar (total: 3.2s)

sample19.0ms

Algorithm
intervals
Results
9.0ms268×body80valid

simplify5.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0177
1217
2217

prune2.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 23.4b

localize9.0ms

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:
4.0ms
(+ (* 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)))

series109.0ms

Counts
2 → 6
Calls
2 calls:
32.0ms
(+ (* 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)))

simplify85.0ms

Algorithm
egg-herbie
Counts
53 → 53
Iterations

Useful iterations: 2 (24.0ms)

IterNodesCost
0244458
1872411
23164403
35001403

prune152.0ms

Filtered
53 candidates to 44 candidates (83.0%)
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))

rewrite27.0ms

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))
11.0ms
(* (/ 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))

series371.0ms

Counts
4 → 12
Calls
4 calls:
36.0ms
(fma x.re y.re (* x.im y.im))
52.0ms
(/ 1 (* (hypot y.re y.im) 1))
174.0ms
(* (/ 1 (* (hypot y.re y.im) 1)) (/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1)))
109.0ms
(/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1))

simplify49.0ms

Algorithm
egg-herbie
Counts
157 → 157
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
04861191
11654892
25002884

prune281.0ms

Filtered
157 candidates to 77 candidates (49.0%)
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))

rewrite14.0ms

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))

series262.0ms

Counts
3 → 9
Calls
3 calls:
36.0ms
(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)) (* (hypot y.re y.im) 1))
110.0ms
(/ (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 (67.0ms)

IterNodesCost
0297767
11133677
23251677
35001670

prune265.0ms

Filtered
98 candidates to 76 candidates (77.6%)
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
(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)) (/ 1 (hypot y.re y.im))))
13.7b
(* (fma x.re y.re (* x.im y.im)) (/ 1 (hypot y.re y.im)))

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
208×add-exp-log
130×prod-exp
58×div-exp
50×add-cbrt-cube
47×1-exp
29×rec-exp
23×add-sqr-sqrt
21×cbrt-unprod
17×*-un-lft-identity times-frac
16×add-cube-cbrt
14×pow1 associate-*r*
12×cbrt-undiv
10×associate-*l*
5×associate-*r/ pow-prod-down
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×un-div-inv div-inv associate-/l* unswap-sqr
2×frac-times pow-flip *-commutative
1×frac-2neg associate-*l/ clear-num associate-/r* fma-udef inv-pow
Counts
4 → 165
Calls
4 calls:
1.0ms
(fma x.re y.re (* x.im y.im))
5.0ms
(/ 1 (* (hypot y.re y.im) 1))
13.0ms
(* (/ 1 (* (hypot y.re y.im) 1)) (* (fma x.re y.re (* x.im y.im)) (/ 1 (hypot y.re y.im))))
7.0ms
(* (fma x.re y.re (* x.im y.im)) (/ 1 (hypot y.re y.im)))

series378.0ms

Counts
4 → 12
Calls
4 calls:
36.0ms
(fma x.re y.re (* x.im y.im))
53.0ms
(/ 1 (* (hypot y.re y.im) 1))
177.0ms
(* (/ 1 (* (hypot y.re y.im) 1)) (* (fma x.re y.re (* x.im y.im)) (/ 1 (hypot y.re y.im))))
112.0ms
(* (fma x.re y.re (* x.im y.im)) (/ 1 (hypot y.re y.im)))

simplify48.0ms

Algorithm
egg-herbie
Counts
177 → 177
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
05861348
11918993
25001973

prune261.0ms

Filtered
177 candidates to 79 candidates (44.6%)
Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 6.8b

regimes157.0ms

Accuracy

18.8% (9.2b remaining)

Error of 15.1b against oracle of 6.0b and baseline of 17.2b

bsearch46.0ms

Steps
ItersRangePoint
10
1.464110213656478e+115
6.0573437940032564e+125
5.882312647988265e+125

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01910
12110
22110

end0.0ms

sample525.0ms

Algorithm
intervals
Results
310.0ms8456×body80valid