Details

Time bar (total: 3.7s)

sample25.0ms

Algorithm
intervals
Results
6.0ms201×body80valid
5.0ms25×body2560valid
2.0ms7×body5120valid
2.0ms10×body1280valid
1.0ms10×body640valid
0.0ms2×body320valid
0.0ms1×body160valid

simplify6.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0248
1308
2338
3338

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.8b

localize10.0ms

Local error

Found 3 expressions with local error:

0.2b
(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
0.3b
(+ (sqrt (+ (* re re) (* im im))) re)
31.8b
(sqrt (+ (* re re) (* im im)))

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
8×*-un-lft-identity
7×pow1 add-sqr-sqrt sqrt-prod
6×add-cube-cbrt fma-def
5×add-log-exp
4×sqrt-div
3×add-exp-log expm1-log1p-u sqrt-pow1 flip3-+ add-cbrt-cube flip-+ log1p-expm1-u
2×pow1/2 associate-*r/
1×+-commutative rem-sqrt-square pow-prod-down sum-log hypot-def distribute-lft-out
Counts
3 → 53
Calls
3 calls:
9.0ms
(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
7.0ms
(+ (sqrt (+ (* re re) (* im im))) re)
4.0ms
(sqrt (+ (* re re) (* im im)))

series266.0ms

Counts
3 → 9
Calls
3 calls:
180.0ms
(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
45.0ms
(+ (sqrt (+ (* re re) (* im im))) re)
40.0ms
(sqrt (+ (* re re) (* im im)))

simplify77.0ms

Algorithm
egg-herbie
Counts
62 → 62
Iterations

Useful iterations: 3 (66.0ms)

IterNodesCost
0264372
1830337
22660322
35002320

prune182.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 5.5b

localize9.0ms

Local error

Found 2 expressions with local error:

0.2b
(sqrt (* 2.0 (* 1 (+ re (hypot re im)))))
0.3b
(+ re (hypot re im))

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
8×pow1
5×*-un-lft-identity
4×associate-*r/ add-log-exp
3×add-sqr-sqrt add-cube-cbrt fma-def sqrt-pow1 pow-prod-down
2×add-exp-log expm1-log1p-u flip3-+ sqrt-div add-cbrt-cube flip-+ log1p-expm1-u
1×+-commutative pow1/2 sum-log sqrt-prod distribute-lft-out
Counts
2 → 33
Calls
2 calls:
7.0ms
(sqrt (* 2.0 (* 1 (+ re (hypot re im)))))
3.0ms
(+ re (hypot re im))

series257.0ms

Counts
2 → 6
Calls
2 calls:
201.0ms
(sqrt (* 2.0 (* 1 (+ re (hypot re im)))))
56.0ms
(+ re (hypot re im))

simplify81.0ms

Algorithm
egg-herbie
Counts
39 → 39
Iterations

Useful iterations: 2 (20.0ms)

IterNodesCost
0194185
1791167
23233161
35001161

prune116.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 5.5b

localize8.0ms

Local error

Found 3 expressions with local error:

0.2b
(sqrt (+ re (hypot re im)))
0.3b
(+ re (hypot re im))
0.4b
(* (sqrt 2.0) (sqrt (+ re (hypot re im))))

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
15×*-un-lft-identity sqrt-prod
9×add-cube-cbrt
8×pow1
7×associate-*r*
6×associate-*l*
5×add-exp-log add-cbrt-cube add-log-exp
4×sqrt-div unswap-sqr
3×expm1-log1p-u fma-def sqrt-pow1 flip3-+ pow1/2 pow-prod-down flip-+ log1p-expm1-u distribute-lft-out
2×associate-*r/
1×+-commutative rem-sqrt-square sqrt-unprod prod-exp sum-log *-commutative cbrt-unprod hypot-def
Counts
3 → 71
Calls
3 calls:
3.0ms
(sqrt (+ re (hypot re im)))
3.0ms
(+ re (hypot re im))
8.0ms
(* (sqrt 2.0) (sqrt (+ re (hypot re im))))

series387.0ms

Counts
3 → 9
Calls
3 calls:
127.0ms
(sqrt (+ re (hypot re im)))
63.0ms
(+ re (hypot re im))
197.0ms
(* (sqrt 2.0) (sqrt (+ re (hypot re im))))

simplify113.0ms

Algorithm
egg-herbie
Counts
80 → 80
Iterations

Useful iterations: 2 (28.0ms)

IterNodesCost
0288432
1992402
24306387
35001387

prune204.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 5.3b

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b
(sqrt (+ re (hypot re im)))
0.3b
(+ re (hypot re im))
0.3b
(* (sqrt (sqrt 2.0)) (sqrt (+ re (hypot re im))))
0.3b
(* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) (sqrt (+ re (hypot re im)))))

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
35×sqrt-prod
29×add-sqr-sqrt
20×*-un-lft-identity
18×associate-*l*
17×pow1
14×add-cube-cbrt
11×add-exp-log add-cbrt-cube
10×pow-prod-down
8×associate-*r*
6×sqrt-pow1 pow1/2 sqrt-div associate-*r/ add-log-exp unswap-sqr
4×expm1-log1p-u flip3-+ prod-exp cbrt-unprod flip-+ log1p-expm1-u
3×fma-def sqrt-unprod distribute-lft-out
2×*-commutative
1×+-commutative rem-sqrt-square sum-log hypot-def
Counts
4 → 107
Calls
4 calls:
4.0ms
(sqrt (+ re (hypot re im)))
3.0ms
(+ re (hypot re im))
10.0ms
(* (sqrt (sqrt 2.0)) (sqrt (+ re (hypot re im))))
13.0ms
(* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) (sqrt (+ re (hypot re im)))))

series658.0ms

Counts
4 → 12
Calls
4 calls:
135.0ms
(sqrt (+ re (hypot re im)))
56.0ms
(+ re (hypot re im))
262.0ms
(* (sqrt (sqrt 2.0)) (sqrt (+ re (hypot re im))))
205.0ms
(* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) (sqrt (+ re (hypot re im)))))

simplify47.0ms

Algorithm
egg-herbie
Counts
119 → 119
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
0405828
11591742
25002725

prune326.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 5.3b

regimes88.0ms

Accuracy

30.2% (4.1b remaining)

Error of 11.5b against oracle of 7.4b and baseline of 13.3b

bsearch74.0ms

Steps
ItersRangePoint
7
-1.0114733541290617e-38
-2.5734052351795068e-40
-9.259771162716737e-39
3
-1.4509995558059801e+125
-1.140406744705429e+125
-1.2762910995619203e+125
2
-6.814808586201778e+164
-5.701746713112747e+164
-5.840879447248876e+164

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 1 (1.0ms)

IterNodesCost
03726
14213
24513
34513

end0.0ms

sample675.0ms

Algorithm
intervals
Results
201.0ms6029×body80valid
144.0ms715×body2560valid
74.0ms471×body1280valid
66.0ms270×body5120valid
35.0ms281×body640valid
14.0ms151×body320valid
5.0ms83×body160valid