Details

Time bar (total: 7.3s)

sample432.0ms

Algorithm
intervals
Results
41.0ms52×body640valid
38.0ms68×body1280valid
23.0ms264×body80valid
6.0ms24×body320valid
0.0ms2×body160valid

simplify41.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
03521
16317
29817
321717
489517
5500117

prune17.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 37.6b

localize27.0ms

Local error

Found 4 expressions with local error:

1.8b
(* (atan2 x.im x.re) y.im)
33.5b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.5b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
34.4b
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite53.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
8×pow1 add-cube-cbrt *-un-lft-identity
6×add-exp-log sqrt-prod add-cbrt-cube
4×expm1-log1p-u sqrt-div log1p-expm1-u add-log-exp
3×associate-*r* associate-*l*
2×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+ hypot-def
1×cos-sum pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
4 → 66
Calls
4 calls:
7.0ms
(* (atan2 x.im x.re) y.im)
8.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
8.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
27.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series225.0ms

Counts
4 → 12
Calls
4 calls:
18.0ms
(* (atan2 x.im x.re) y.im)
32.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
32.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
143.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify80.0ms

Algorithm
egg-herbie
Counts
78 → 78
Iterations

Useful iterations: 2 (14.0ms)

IterNodesCost
0207456
1556415
21286411
32863411
45002411

prune383.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 23.2b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))
0.3b
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
1.8b
(* (atan2 x.im x.re) y.im)
33.5b
(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
11×pow1
9×add-cube-cbrt *-un-lft-identity associate-*l*
8×add-exp-log add-cbrt-cube
6×associate-*r* add-log-exp
4×expm1-log1p-u log1p-expm1-u
3×sqrt-prod log-pow
2×sqrt-pow1 pow1/2 sqrt-div pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×sub-neg rem-sqrt-square flip3-- flip3-+ fma-neg diff-log prod-diff flip-- flip-+ hypot-def
Counts
4 → 77
Calls
4 calls:
9.0ms
(- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))
15.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
7.0ms
(* (atan2 x.im x.re) y.im)
8.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

series246.0ms

Counts
4 → 12
Calls
4 calls:
116.0ms
(- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))
82.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
15.0ms
(* (atan2 x.im x.re) y.im)
33.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify83.0ms

Algorithm
egg-herbie
Counts
89 → 89
Iterations

Useful iterations: 3 (76.0ms)

IterNodesCost
0320595
11020544
23156516
35001484

prune319.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 3.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b
(fma y.re (log (hypot x.re x.im)) (- (* (atan2 x.im x.re) y.im)))
0.2b
(pow (fma y.re (log (hypot x.re x.im)) (- (* (atan2 x.im x.re) y.im))) 3)
1.8b
(* (atan2 x.im x.re) y.im)
40.5b
(cbrt (pow (fma y.re (log (hypot x.re x.im)) (- (* (atan2 x.im x.re) y.im))) 3))

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
12×cbrt-prod add-cube-cbrt *-un-lft-identity
7×pow1 add-exp-log add-cbrt-cube
6×unpow-prod-down cube-prod
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×pow-unpow associate-*r* associate-*l*
2×cube-mult unpow3 sqr-pow
1×pow-to-exp pow-pow pow1/3 pow-prod-down pow-exp prod-exp *-commutative rem-cbrt-cube cbrt-unprod fma-udef rem-cube-cbrt unswap-sqr
Counts
4 → 78
Calls
4 calls:
0.0ms
(fma y.re (log (hypot x.re x.im)) (- (* (atan2 x.im x.re) y.im)))
3.0ms
(pow (fma y.re (log (hypot x.re x.im)) (- (* (atan2 x.im x.re) y.im))) 3)
9.0ms
(* (atan2 x.im x.re) y.im)
2.0ms
(cbrt (pow (fma y.re (log (hypot x.re x.im)) (- (* (atan2 x.im x.re) y.im))) 3))

series520.0ms

Counts
4 → 12
Calls
4 calls:
118.0ms
(fma y.re (log (hypot x.re x.im)) (- (* (atan2 x.im x.re) y.im)))
267.0ms
(pow (fma y.re (log (hypot x.re x.im)) (- (* (atan2 x.im x.re) y.im))) 3)
15.0ms
(* (atan2 x.im x.re) y.im)
120.0ms
(cbrt (pow (fma y.re (log (hypot x.re x.im)) (- (* (atan2 x.im x.re) y.im))) 3))

simplify49.0ms

Algorithm
egg-herbie
Counts
90 → 90
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
0299737
11300693
25002683

prune322.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 3.0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b
(fma y.re (log (hypot x.re x.im)) (- (* (atan2 x.im x.re) y.im)))
0.2b
(pow (fma y.re (log (hypot x.re x.im)) (- (* (atan2 x.im x.re) y.im))) 3)
1.6b
(log (exp (pow (fma y.re (log (hypot x.re x.im)) (- (* (atan2 x.im x.re) y.im))) 3)))
1.8b
(* (atan2 x.im x.re) y.im)

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
15×add-sqr-sqrt
13×add-cube-cbrt *-un-lft-identity log-pow
12×exp-prod
8×pow1
7×add-exp-log add-cbrt-cube
6×unpow-prod-down cube-prod
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×pow-unpow log-prod associate-*r* associate-*l*
2×cube-mult unpow3 sqr-pow
1×pow-to-exp pow-pow rem-log-exp pow-prod-down pow-exp prod-exp *-commutative cbrt-unprod fma-udef rem-cube-cbrt unswap-sqr
Counts
4 → 81
Calls
4 calls:
0.0ms
(fma y.re (log (hypot x.re x.im)) (- (* (atan2 x.im x.re) y.im)))
3.0ms
(pow (fma y.re (log (hypot x.re x.im)) (- (* (atan2 x.im x.re) y.im))) 3)
7.0ms
(log (exp (pow (fma y.re (log (hypot x.re x.im)) (- (* (atan2 x.im x.re) y.im))) 3)))
7.0ms
(* (atan2 x.im x.re) y.im)

series665.0ms

Counts
4 → 12
Calls
4 calls:
121.0ms
(fma y.re (log (hypot x.re x.im)) (- (* (atan2 x.im x.re) y.im)))
263.0ms
(pow (fma y.re (log (hypot x.re x.im)) (- (* (atan2 x.im x.re) y.im))) 3)
262.0ms
(log (exp (pow (fma y.re (log (hypot x.re x.im)) (- (* (atan2 x.im x.re) y.im))) 3)))
19.0ms
(* (atan2 x.im x.re) y.im)

simplify54.0ms

Algorithm
egg-herbie
Counts
93 → 93
Iterations

Useful iterations: 2 (41.0ms)

IterNodesCost
0321750
11314657
25001646

prune371.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 3.0b

regimes193.0ms

Accuracy

0% (0.6b remaining)

Error of 4.0b against oracle of 3.4b and baseline of 4.0b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0249
1289
2289

end0.0ms

sample3.1s

Algorithm
intervals
Results
1.1s2018×body1280valid
647.0ms7976×body80valid
556.0ms1497×body640valid
165.0ms637×body320valid
56.0ms314×body160valid