Details

Time bar (total: 3.5s)

sample22.0ms

Algorithm
intervals
Results
12.0ms270×body80valid

simplify13.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0217
1407
2567
3767
4907
5947
6947

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.9b

localize10.0ms

Local error

Found 2 expressions with local error:

0.2b
(- (* x.im y.re) (* x.re y.im))
26.5b
(/ (- (* x.im y.re) (* x.re 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×associate-/r* associate-/l*
2×pow1 expm1-log1p-u flip3-- associate-/r/ flip-- log1p-expm1-u associate-/l/
1×cbrt-undiv sub-neg frac-2neg flip3-+ fma-neg diff-log div-sub div-exp prod-diff clear-num flip-+ div-inv
Counts
2 → 50
Calls
2 calls:
3.0ms
(- (* x.im y.re) (* x.re y.im))
10.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

series125.0ms

Counts
2 → 6
Calls
2 calls:
37.0ms
(- (* x.im y.re) (* x.re y.im))
89.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify104.0ms

Algorithm
egg-herbie
Counts
56 → 56
Iterations

Useful iterations: 3 (98.0ms)

IterNodesCost
0270481
11012432
23842422
35001421

prune160.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 14.4b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1 (* (hypot y.re y.im) 1))
0.2b
(- (* x.im y.re) (* x.re y.im))
0.2b
(* (/ 1 (* (hypot y.re y.im) 1)) (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)))
17.3b
(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

rewrite44.0ms

Algorithm
rewrite-expression-head
Rules
83×add-exp-log
38×prod-exp
32×add-cbrt-cube
29×div-exp
28×add-sqr-sqrt
25×times-frac
23×add-cube-cbrt *-un-lft-identity
18×1-exp
13×associate-*r*
10×cbrt-undiv
9×pow1 rec-exp cbrt-unprod
7×associate-*l*
6×associate-/l* add-log-exp
4×expm1-log1p-u associate-/r* log1p-expm1-u div-inv
2×flip3-- pow-flip frac-2neg pow-prod-down clear-num flip-- associate-/l/ unswap-sqr
1×frac-times sub-neg fma-neg diff-log div-sub associate-*r/ prod-diff associate-*l/ *-commutative inv-pow
Counts
4 → 143
Calls
4 calls:
4.0ms
(/ 1 (* (hypot y.re y.im) 1))
3.0ms
(- (* x.im y.re) (* x.re y.im))
26.0ms
(* (/ 1 (* (hypot y.re y.im) 1)) (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)))
7.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

series384.0ms

Counts
4 → 12
Calls
4 calls:
52.0ms
(/ 1 (* (hypot y.re y.im) 1))
38.0ms
(- (* x.im y.re) (* x.re y.im))
181.0ms
(* (/ 1 (* (hypot y.re y.im) 1)) (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)))
113.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

simplify66.0ms

Algorithm
egg-herbie
Counts
155 → 155
Iterations

Useful iterations: 2 (50.0ms)

IterNodesCost
05551207
123061003
25003995

prune335.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.2b

localize9.0ms

Local error

Found 3 expressions with local error:

0.1b
(/ (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)) (hypot y.re y.im))
0.2b
(- (* x.im y.re) (* x.re y.im))
17.3b
(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
84×times-frac
53×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
16×associate-/l*
10×add-exp-log add-cbrt-cube
6×associate-/r* div-inv
5×add-log-exp
4×cbrt-undiv div-exp
3×pow1 expm1-log1p-u div-sub log1p-expm1-u associate-/l/
2×flip3-- frac-2neg clear-num flip--
1×sub-neg fma-neg diff-log prod-diff
Counts
3 → 121
Calls
3 calls:
9.0ms
(/ (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)) (hypot y.re y.im))
3.0ms
(- (* x.im y.re) (* x.re y.im))
7.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

series266.0ms

Counts
3 → 9
Calls
3 calls:
115.0ms
(/ (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)) (hypot y.re y.im))
38.0ms
(- (* x.im y.re) (* x.re y.im))
112.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

simplify54.0ms

Algorithm
egg-herbie
Counts
130 → 130
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
04511408
116591307
250011298

prune337.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.2b

localize11.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (/ (* x.im y.re) (hypot y.re y.im)) (hypot y.re y.im))
1.3b
(/ (/ (* x.re y.im) (hypot y.re y.im)) (hypot y.re y.im))
8.8b
(/ (* x.re y.im) (hypot y.re y.im))
12.0b
(/ (* x.im y.re) (hypot y.re y.im))

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
72×times-frac
40×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
32×add-exp-log add-cbrt-cube
16×associate-/l*
14×cbrt-undiv div-exp
12×associate-/r* div-inv
4×pow1 expm1-log1p-u frac-2neg prod-exp clear-num cbrt-unprod log1p-expm1-u add-log-exp
2×associate-/l/
Counts
4 → 146
Calls
4 calls:
5.0ms
(/ (/ (* x.im y.re) (hypot y.re y.im)) (hypot y.re y.im))
8.0ms
(/ (/ (* x.re y.im) (hypot y.re y.im)) (hypot y.re y.im))
3.0ms
(/ (* x.re y.im) (hypot y.re y.im))
3.0ms
(/ (* x.im y.re) (hypot y.re y.im))

series278.0ms

Counts
4 → 12
Calls
4 calls:
70.0ms
(/ (/ (* x.im y.re) (hypot y.re y.im)) (hypot y.re y.im))
70.0ms
(/ (/ (* x.re y.im) (hypot y.re y.im)) (hypot y.re y.im))
70.0ms
(/ (* x.re y.im) (hypot y.re y.im))
67.0ms
(/ (* x.im y.re) (hypot y.re y.im))

simplify56.0ms

Algorithm
egg-herbie
Counts
158 → 158
Iterations

Useful iterations: 2 (44.0ms)

IterNodesCost
04951158
121661010
25001996

prune384.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.3b

regimes179.0ms

Accuracy

53.4% (4.1b remaining)

Error of 4.8b against oracle of 0.7b and baseline of 9.6b

bsearch64.0ms

Steps
ItersRangePoint
6
1.3790358199987548e+83
1.4715590077997302e+84
2.1803868185679244e+83
6
-1.4880664606886953e+122
-2.11216914075069e+121
-1.362512780340662e+122

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03122
13122

end0.0ms

sample532.0ms

Algorithm
intervals
Results
307.0ms8480×body80valid