Details

Time bar (total: 7.2s)

sample367.0ms

Algorithm
intervals
Results
39.0ms62×body1280valid
21.0ms248×body80valid
19.0ms49×body640valid
6.0ms21×body320valid
2.0ms10×body160valid

simplify40.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
03521
16317
29817
321717
489517
5500117

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.7b

localize24.0ms

Local error

Found 4 expressions with local error:

1.9b
(* (atan2 x.im x.re) y.im)
28.8b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
28.8b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
33.3b
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite21.0ms

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:
3.0ms
(* (atan2 x.im x.re) y.im)
3.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
3.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
8.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series234.0ms

Counts
4 → 12
Calls
4 calls:
16.0ms
(* (atan2 x.im x.re) y.im)
34.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
36.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
148.0ms
(cos (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify85.0ms

Algorithm
egg-herbie
Counts
78 → 78
Iterations

Useful iterations: 2 (14.0ms)

IterNodesCost
0207456
1556415
21286411
32863411
45002411

prune377.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 20.3b

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)
1.9b
(* (atan2 x.im x.re) y.im)
28.8b
(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite16.0ms

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:
3.0ms
(- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))
5.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
3.0ms
(* (atan2 x.im x.re) y.im)
4.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

series259.0ms

Counts
4 → 12
Calls
4 calls:
118.0ms
(- (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re) (* (atan2 x.im x.re) y.im))
88.0ms
(* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.re)
16.0ms
(* (atan2 x.im x.re) y.im)
37.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify86.0ms

Algorithm
egg-herbie
Counts
89 → 89
Iterations

Useful iterations: 3 (76.0ms)

IterNodesCost
0320595
11020544
23156516
35001484

prune313.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 4.0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b
(fma y.re (log (hypot x.re x.im)) (- (* (atan2 x.im x.re) y.im)))
0.3b
(pow (fma y.re (log (hypot x.re x.im)) (- (* (atan2 x.im x.re) y.im))) 3)
1.9b
(* (atan2 x.im x.re) y.im)
38.0b
(cbrt (pow (fma y.re (log (hypot x.re x.im)) (- (* (atan2 x.im x.re) y.im))) 3))

rewrite7.0ms

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)))
1.0ms
(pow (fma y.re (log (hypot x.re x.im)) (- (* (atan2 x.im x.re) y.im))) 3)
3.0ms
(* (atan2 x.im x.re) y.im)
1.0ms
(cbrt (pow (fma y.re (log (hypot x.re x.im)) (- (* (atan2 x.im x.re) y.im))) 3))

series546.0ms

Counts
4 → 12
Calls
4 calls:
128.0ms
(fma y.re (log (hypot x.re x.im)) (- (* (atan2 x.im x.re) y.im)))
278.0ms
(pow (fma y.re (log (hypot x.re x.im)) (- (* (atan2 x.im x.re) y.im))) 3)
16.0ms
(* (atan2 x.im x.re) y.im)
125.0ms
(cbrt (pow (fma y.re (log (hypot x.re x.im)) (- (* (atan2 x.im x.re) y.im))) 3))

simplify50.0ms

Algorithm
egg-herbie
Counts
90 → 90
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
0299737
11300693
25002683

prune318.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 4.0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b
(fma y.re (log (hypot x.re x.im)) (- (* (atan2 x.im x.re) y.im)))
0.3b
(pow (fma y.re (log (hypot x.re x.im)) (- (* (atan2 x.im x.re) y.im))) 3)
1.9b
(* (atan2 x.im x.re) y.im)
13.0b
(cbrt (log1p (expm1 (pow (fma y.re (log (hypot x.re x.im)) (- (* (atan2 x.im x.re) y.im))) 3))))

rewrite6.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
10×add-cube-cbrt *-un-lft-identity
7×pow1 add-exp-log add-cbrt-cube
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×cbrt-prod unpow-prod-down pow-unpow cube-prod associate-*r* associate-*l*
1×cube-mult pow-to-exp pow-pow pow1/3 unpow3 pow-prod-down pow-exp prod-exp *-commutative cbrt-unprod fma-udef rem-cube-cbrt unswap-sqr sqr-pow
Counts
4 → 68
Calls
4 calls:
0.0ms
(fma y.re (log (hypot x.re x.im)) (- (* (atan2 x.im x.re) y.im)))
1.0ms
(pow (fma y.re (log (hypot x.re x.im)) (- (* (atan2 x.im x.re) y.im))) 3)
3.0ms
(* (atan2 x.im x.re) y.im)
1.0ms
(cbrt (log1p (expm1 (pow (fma y.re (log (hypot x.re x.im)) (- (* (atan2 x.im x.re) y.im))) 3))))

series839.0ms

Counts
4 → 12
Calls
4 calls:
130.0ms
(fma y.re (log (hypot x.re x.im)) (- (* (atan2 x.im x.re) y.im)))
281.0ms
(pow (fma y.re (log (hypot x.re x.im)) (- (* (atan2 x.im x.re) y.im))) 3)
16.0ms
(* (atan2 x.im x.re) y.im)
411.0ms
(cbrt (log1p (expm1 (pow (fma y.re (log (hypot x.re x.im)) (- (* (atan2 x.im x.re) y.im))) 3))))

simplify57.0ms

Algorithm
egg-herbie
Counts
80 → 80
Iterations

Useful iterations: 2 (49.0ms)

IterNodesCost
0388661
11687607
25001600

prune337.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 4.0b

regimes148.0ms

Accuracy

0% (0.5b remaining)

Error of 4.0b against oracle of 3.5b and baseline of 4.0b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02611
13011
23011

end0.0ms

sample3.0s

Algorithm
intervals
Results
1.2s1989×body1280valid
679.0ms7977×body80valid
566.0ms1423×body640valid
181.0ms656×body320valid
55.0ms296×body160valid