Details

Time bar (total: 3.3s)

sample20.0ms

Algorithm
intervals
Results
9.0ms271×body80valid

simplify12.0ms

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: 28.3b

localize9.0ms

Local error

Found 2 expressions with local error:

0.5b
(- (* x.im y.re) (* x.re y.im))
27.8b
(/ (- (* 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)))

series119.0ms

Counts
2 → 6
Calls
2 calls:
37.0ms
(- (* x.im y.re) (* x.re y.im))
82.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify101.0ms

Algorithm
egg-herbie
Counts
56 → 56
Iterations

Useful iterations: 3 (95.0ms)

IterNodesCost
0270481
11012432
23842422
35001421

prune152.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 14.4b

localize11.0ms

Local error

Found 3 expressions with local error:

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))

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
67×add-exp-log
32×prod-exp
26×add-cbrt-cube
25×add-sqr-sqrt
23×div-exp
22×times-frac
20×add-cube-cbrt *-un-lft-identity
13×associate-*r*
12×1-exp
8×cbrt-undiv cbrt-unprod
7×associate-*l*
6×rec-exp
5×pow1 add-log-exp
3×expm1-log1p-u associate-/r* log1p-expm1-u div-inv associate-/l*
2×flip3-- flip-- associate-/l/ unswap-sqr
1×frac-times sub-neg frac-2neg fma-neg diff-log div-sub associate-*r/ prod-diff pow-prod-down associate-*l/ clear-num *-commutative
Counts
3 → 110
Calls
3 calls:
24.0ms
(* (/ 1 (* (hypot y.re y.im) 1)) (/ (- (* x.im y.re) (* x.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))

series329.0ms

Counts
3 → 9
Calls
3 calls:
182.0ms
(* (/ 1 (* (hypot y.re y.im) 1)) (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)))
35.0ms
(- (* x.im y.re) (* x.re y.im))
113.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

simplify59.0ms

Algorithm
egg-herbie
Counts
119 → 119
Iterations

Useful iterations: 2 (48.0ms)

IterNodesCost
05371095
12236907
25002905

prune264.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.7b

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

rewrite26.0ms

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))
10.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

series262.0ms

Counts
3 → 9
Calls
3 calls:
114.0ms
(/ (/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im)) (hypot y.re y.im))
35.0ms
(- (* x.im y.re) (* x.re y.im))
113.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (hypot y.re y.im))

simplify50.0ms

Algorithm
egg-herbie
Counts
130 → 130
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
04511408
116591307
250011298

prune327.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.6b

localize12.0ms

Local error

Found 3 expressions with local error:

0.2b
(* (/ 1 (* (hypot y.re y.im) 1)) (/ (fma x.im y.re (- (* x.re y.im))) (hypot y.re y.im)))
0.3b
(fma x.im y.re (- (* x.re y.im)))
17.3b
(/ (fma x.im y.re (- (* x.re y.im))) (hypot y.re y.im))

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
67×add-exp-log
32×prod-exp
26×add-cbrt-cube
25×add-sqr-sqrt
23×div-exp
22×times-frac
20×add-cube-cbrt *-un-lft-identity
13×associate-*r*
12×1-exp
8×cbrt-undiv cbrt-unprod
7×associate-*l*
6×rec-exp
5×pow1
3×expm1-log1p-u associate-/r* log1p-expm1-u div-inv associate-/l* add-log-exp
2×unswap-sqr
1×frac-times frac-2neg associate-*r/ pow-prod-down associate-*l/ clear-num *-commutative fma-udef
Counts
3 → 101
Calls
3 calls:
20.0ms
(* (/ 1 (* (hypot y.re y.im) 1)) (/ (fma x.im y.re (- (* x.re y.im))) (hypot y.re y.im)))
0.0ms
(fma x.im y.re (- (* x.re y.im)))
2.0ms
(/ (fma x.im y.re (- (* x.re y.im))) (hypot y.re y.im))

series350.0ms

Counts
3 → 9
Calls
3 calls:
184.0ms
(* (/ 1 (* (hypot y.re y.im) 1)) (/ (fma x.im y.re (- (* x.re y.im))) (hypot y.re y.im)))
43.0ms
(fma x.im y.re (- (* x.re y.im)))
123.0ms
(/ (fma x.im y.re (- (* x.re y.im))) (hypot y.re y.im))

simplify52.0ms

Algorithm
egg-herbie
Counts
110 → 110
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
04271037
11749853
25002851

prune244.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.6b

regimes171.0ms

Accuracy

28.1% (8.8b remaining)

Error of 13.3b against oracle of 4.5b and baseline of 16.7b

bsearch86.0ms

Steps
ItersRangePoint
9
6.479814166339293e+202
2.7363046317489248e+212
6.602179941996442e+202
9
-2.886273399460008e+138
-2.6889041873995e+131
-2.8763806766248217e+136

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03414
14014
24114
34114

end0.0ms

sample529.0ms

Algorithm
intervals
Results
305.0ms8457×body80valid