Details

Time bar (total: 4.2s)

sample20.0ms

Algorithm
intervals
Results
9.0ms270×body80valid

simplify13.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0217
1407
2567
3767
4907
5947
6947

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.0b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* y.re y.re) (* y.im y.im))
0.5b
(- (* 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)))

rewrite18.0ms

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
3×pow1 expm1-log1p-u associate-/r* log1p-expm1-u associate-/l*
2×flip3-- flip3-+ associate-/r/ flip-- flip-+ associate-/l/
1×cbrt-undiv +-commutative sub-neg fma-def frac-2neg fma-neg diff-log div-sub div-exp prod-diff clear-num sum-log div-inv
Counts
3 → 64
Calls
3 calls:
4.0ms
(+ (* y.re y.re) (* y.im y.im))
4.0ms
(- (* x.im y.re) (* x.re y.im))
8.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

series152.0ms

Counts
3 → 9
Calls
3 calls:
27.0ms
(+ (* y.re y.re) (* y.im y.im))
36.0ms
(- (* x.im y.re) (* x.re y.im))
88.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify39.0ms

Algorithm
egg-herbie
Counts
73 → 73
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
0316555
11343496
25001481

prune209.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 13.1b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(hypot y.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)))
0.5b
(- (* x.im y.re) (* x.re y.im))
17.3b
(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
68×add-exp-log
32×prod-exp
27×add-cbrt-cube
26×add-sqr-sqrt
23×div-exp
22×times-frac
21×add-cube-cbrt *-un-lft-identity
13×associate-*r*
12×1-exp
8×cbrt-undiv cbrt-unprod
7×associate-*l*
6×pow1 rec-exp add-log-exp
4×expm1-log1p-u log1p-expm1-u
3×associate-/r* div-inv associate-/l*
2×flip3-- flip-- associate-/l/ unswap-sqr
1×frac-times sub-neg hypot-udef frac-2neg fma-neg diff-log div-sub associate-*r/ prod-diff pow-prod-down associate-*l/ clear-num *-commutative
Counts
4 → 120
Calls
4 calls:
1.0ms
(hypot y.re y.im)
13.0ms
(* (/ 1 (* (hypot y.re y.im) 1)) (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)))
4.0ms
(- (* x.im y.re) (* x.re y.im))
6.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

series384.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(hypot y.re y.im)
183.0ms
(* (/ 1 (* (hypot y.re y.im) 1)) (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)))
37.0ms
(- (* x.im y.re) (* x.re y.im))
116.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

simplify58.0ms

Algorithm
egg-herbie
Counts
132 → 132
Iterations

Useful iterations: 2 (47.0ms)

IterNodesCost
05461122
12249931
25002929

prune323.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.5b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b
(hypot y.re y.im)
0.1b
(/ (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)) (* (hypot y.re y.im) 1))
0.5b
(- (* 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
40×times-frac
26×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
23×add-exp-log
18×add-cbrt-cube
16×associate-/l*
10×div-exp
7×cbrt-undiv
6×add-log-exp
4×pow1 expm1-log1p-u prod-exp associate-/r* log1p-expm1-u div-inv
3×div-sub associate-/l/
2×flip3-- frac-2neg 1-exp clear-num flip-- cbrt-unprod
1×sub-neg hypot-udef fma-neg diff-log prod-diff
Counts
4 → 109
Calls
4 calls:
1.0ms
(hypot y.re y.im)
8.0ms
(/ (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)) (* (hypot y.re y.im) 1))
4.0ms
(- (* x.im y.re) (* x.re y.im))
6.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

series320.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(hypot y.re y.im)
117.0ms
(/ (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)) (* (hypot y.re y.im) 1))
39.0ms
(- (* x.im y.re) (* x.re y.im))
117.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

simplify46.0ms

Algorithm
egg-herbie
Counts
121 → 121
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
0432989
11705876
25001875

prune328.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 5.4b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ 1 (/ (hypot y.re y.im) (- (* x.im y.re) (* x.re y.im)))) (* (hypot y.re y.im) 1))
0.2b
(/ 1 (/ (hypot y.re y.im) (- (* x.im y.re) (* x.re y.im))))
0.5b
(- (* x.im y.re) (* x.re y.im))
17.3b
(/ (hypot y.re y.im) (- (* x.im y.re) (* x.re y.im)))

rewrite49.0ms

Algorithm
rewrite-expression-head
Rules
284×times-frac
130×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
81×add-exp-log
56×associate-/l*
50×div-exp
32×add-cbrt-cube
25×associate-/r/
19×associate-/r*
16×cbrt-undiv
15×1-exp div-inv
14×prod-exp
12×flip3-- flip--
8×rec-exp
6×add-log-exp
5×pow1
4×expm1-log1p-u log1p-expm1-u
3×frac-2neg clear-num cbrt-unprod
1×sub-neg pow-flip fma-neg diff-log prod-diff associate-/l/ inv-pow
Counts
4 → 274
Calls
4 calls:
17.0ms
(/ (/ 1 (/ (hypot y.re y.im) (- (* x.im y.re) (* x.re y.im)))) (* (hypot y.re y.im) 1))
8.0ms
(/ 1 (/ (hypot y.re y.im) (- (* x.im y.re) (* x.re y.im))))
4.0ms
(- (* x.im y.re) (* x.re y.im))
5.0ms
(/ (hypot y.re y.im) (- (* x.im y.re) (* x.re y.im)))

series426.0ms

Counts
4 → 12
Calls
4 calls:
180.0ms
(/ (/ 1 (/ (hypot y.re y.im) (- (* x.im y.re) (* x.re y.im)))) (* (hypot y.re y.im) 1))
115.0ms
(/ 1 (/ (hypot y.re y.im) (- (* x.im y.re) (* x.re y.im))))
39.0ms
(- (* x.im y.re) (* x.re y.im))
92.0ms
(/ (hypot y.re y.im) (- (* x.im y.re) (* x.re y.im)))

simplify104.0ms

Algorithm
egg-herbie
Counts
286 → 286
Iterations

Useful iterations: 2 (70.0ms)

IterNodesCost
09613303
146502898
250012893

prune690.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 5.4b

regimes261.0ms

Accuracy

18.3% (10.0b remaining)

Error of 14.8b against oracle of 4.8b and baseline of 17.0b

bsearch151.0ms

Steps
ItersRangePoint
10
1.7099874871215327e+162
5.4836801255396766e+172
1.725308956868216e+162
8
1.1279014918164225e-148
4.241768331616052e-146
3.550140168299915e-146
5
-2.9125403166450075e-149
-1.0967839700095273e-149
-1.7444252288160641e-149
9
-1.6245779440606675e+159
-2.6703843016992183e+152
-2.982963784965854e+153

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04138
14538
24538

end0.0ms

sample514.0ms

Algorithm
intervals
Results
301.0ms8455×body80valid