Details

Time bar (total: 3.6s)

sample21.0ms

Algorithm
intervals
Results
8.0ms271×body80valid

simplify5.0ms

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: 27.6b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* y.re y.re) (* y.im y.im))
0.5b
(+ (* x.re y.re) (* x.im y.im))
27.1b
(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite50.0ms

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
4×flip3-+ flip-+
3×pow1 expm1-log1p-u associate-/r* log1p-expm1-u associate-/l*
2×+-commutative fma-def sum-log associate-/r/ associate-/l/
1×cbrt-undiv frac-2neg div-exp clear-num div-inv
Counts
3 → 61
Calls
3 calls:
8.0ms
(+ (* y.re y.re) (* y.im y.im))
8.0ms
(+ (* x.re y.re) (* x.im y.im))
33.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

series125.0ms

Counts
3 → 9
Calls
3 calls:
26.0ms
(+ (* y.re y.re) (* y.im y.im))
27.0ms
(+ (* x.re y.re) (* x.im y.im))
72.0ms
(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify132.0ms

Algorithm
egg-herbie
Counts
70 → 70
Iterations

Useful iterations: 2 (30.0ms)

IterNodesCost
0290532
11199475
24872462
35001462

prune187.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 17.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(hypot y.re 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)))
0.5b
(fma x.re y.re (* x.im y.im))
16.5b
(/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1))

rewrite61.0ms

Algorithm
rewrite-expression-head
Rules
155×add-exp-log
86×prod-exp
57×div-exp
45×add-cbrt-cube
35×1-exp
16×cbrt-unprod
14×cbrt-undiv
12×add-sqr-sqrt rec-exp
10×add-cube-cbrt *-un-lft-identity
9×times-frac
7×associate-*r* associate-*l*
6×pow1
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×div-inv associate-/l*
1×frac-times hypot-udef frac-2neg associate-*r/ pow-prod-down associate-*l/ clear-num associate-/r* *-commutative fma-udef unswap-sqr
Counts
4 → 122
Calls
4 calls:
0.0ms
(hypot y.re y.im)
48.0ms
(* (/ 1 (* (hypot y.re y.im) 1)) (/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1)))
0.0ms
(fma x.re y.re (* x.im y.im))
8.0ms
(/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1))

series335.0ms

Counts
4 → 12
Calls
4 calls:
40.0ms
(hypot y.re y.im)
161.0ms
(* (/ 1 (* (hypot y.re y.im) 1)) (/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1)))
33.0ms
(fma x.re y.re (* x.im y.im))
101.0ms
(/ (fma x.re y.re (* x.im y.im)) (* (hypot y.re y.im) 1))

simplify48.0ms

Algorithm
egg-herbie
Counts
134 → 134
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
04861106
11625820
25001818

prune253.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 7.4b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b
(hypot y.re y.im)
0.1b
(/ (/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im)) (* (hypot y.re y.im) 1))
0.5b
(fma x.re y.re (* x.im y.im))
16.5b
(/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im))

rewrite24.0ms

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
4×pow1 expm1-log1p-u prod-exp associate-/r* log1p-expm1-u div-inv add-log-exp
2×frac-2neg 1-exp clear-num cbrt-unprod
1×hypot-udef fma-udef associate-/l/
Counts
4 → 99
Calls
4 calls:
0.0ms
(hypot y.re y.im)
13.0ms
(/ (/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im)) (* (hypot y.re y.im) 1))
0.0ms
(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))

series291.0ms

Counts
4 → 12
Calls
4 calls:
41.0ms
(hypot y.re y.im)
111.0ms
(/ (/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im)) (* (hypot y.re y.im) 1))
34.0ms
(fma x.re y.re (* x.im y.im))
104.0ms
(/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im))

simplify78.0ms

Algorithm
egg-herbie
Counts
111 → 111
Iterations

Useful iterations: 3 (69.0ms)

IterNodesCost
0308794
11149701
23275701
35001693

prune304.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 7.4b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im)) (* (* (sqrt (hypot y.re y.im)) (sqrt (hypot y.re y.im))) 1))
0.5b
(fma x.re y.re (* x.im y.im))
0.5b
(* (sqrt (hypot y.re y.im)) (sqrt (hypot y.re y.im)))
16.5b
(/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im))

rewrite61.0ms

Algorithm
rewrite-expression-head
Rules
46×add-sqr-sqrt
41×add-exp-log
40×times-frac
34×add-cube-cbrt *-un-lft-identity
29×add-cbrt-cube
19×pow1
18×sqrt-prod
16×div-exp associate-/l*
13×prod-exp
10×cbrt-undiv
8×sqrt-pow1 pow1/2 swap-sqr
7×cbrt-unprod
6×associate-*r* associate-*l*
5×pow-prod-up
4×expm1-log1p-u 1-exp associate-/r* log1p-expm1-u div-inv add-log-exp unswap-sqr
3×pow-prod-down pow-sqr
2×frac-2neg clear-num
1×pow2 pow-plus sqrt-unprod rem-square-sqrt *-commutative fma-udef associate-/l/
Counts
4 → 146
Calls
4 calls:
39.0ms
(/ (/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im)) (* (* (sqrt (hypot y.re y.im)) (sqrt (hypot y.re y.im))) 1))
0.0ms
(fma x.re y.re (* x.im y.im))
12.0ms
(* (sqrt (hypot y.re y.im)) (sqrt (hypot y.re y.im)))
5.0ms
(/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im))

series289.0ms

Counts
4 → 12
Calls
4 calls:
106.0ms
(/ (/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im)) (* (* (sqrt (hypot y.re y.im)) (sqrt (hypot y.re y.im))) 1))
37.0ms
(fma x.re y.re (* x.im y.im))
40.0ms
(* (sqrt (hypot y.re y.im)) (sqrt (hypot y.re y.im)))
106.0ms
(/ (fma x.re y.re (* x.im y.im)) (hypot y.re y.im))

simplify73.0ms

Algorithm
egg-herbie
Counts
158 → 158
Iterations

Useful iterations: 2 (61.0ms)

IterNodesCost
04541084
12499890
25001877

prune337.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 7.4b

regimes231.0ms

Accuracy

38.5% (7.2b remaining)

Error of 13.0b against oracle of 5.8b and baseline of 17.5b

bsearch52.0ms

Steps
ItersRangePoint
8
1.5391317150389775e+120
2.0067777917390584e+123
3.9066728708882944e+121
6
-7.1208808412115464e+134
-1.325272421849221e+134
-1.6980297389042706e+134

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02714
13014
23014

end0.0ms

sample550.0ms

Algorithm
intervals
Results
275.0ms8510×body80valid