Details

Time bar (total: 4.2s)

sample27.0ms

Algorithm
intervals
Results
7.0ms194×body80valid
4.0ms22×body2560valid
3.0ms13×body5120valid
2.0ms14×body1280valid
1.0ms8×body640valid
0.0ms5×body320valid

simplify8.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0178
1248
2308
3358
4358

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.4b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
0.0b
(+ (* re re) (* im im))
0.0b
(- (sqrt (+ (* re re) (* im im))) re)
30.5b
(sqrt (+ (* re re) (* im im)))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
8×pow1 add-log-exp
7×*-un-lft-identity
5×add-cube-cbrt sqrt-prod
4×add-exp-log sqrt-div add-cbrt-cube
3×sqrt-pow1
2×flip3-- flip3-+ pow1/2 associate-*r/ flip-- flip-+ difference-of-squares
1×+-commutative sub-neg rem-sqrt-square diff-log pow-prod-down sum-log distribute-lft-out--
Counts
4 → 54
Calls
4 calls:
8.0ms
(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
4.0ms
(+ (* re re) (* im im))
7.0ms
(- (sqrt (+ (* re re) (* im im))) re)
6.0ms
(sqrt (+ (* re re) (* im im)))

series291.0ms

Counts
4 → 12
Calls
4 calls:
168.0ms
(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
29.0ms
(+ (* re re) (* im im))
45.0ms
(- (sqrt (+ (* re re) (* im im))) re)
49.0ms
(sqrt (+ (* re re) (* im im)))

simplify93.0ms

Algorithm
egg-herbie
Counts
66 → 66
Iterations

Useful iterations: 3 (87.0ms)

IterNodesCost
0258459
1938422
23098412
35001410

prune183.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 18.4b

localize14.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im)))))
5.6b
(- (* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im))))) re)
31.6b
(cbrt (+ (* re re) (* im im)))
31.6b
(cbrt (+ (* re re) (* im im)))

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt
10×cbrt-prod add-cube-cbrt *-un-lft-identity
9×associate-*r*
8×sqrt-prod
6×pow1 add-exp-log cbrt-div add-cbrt-cube add-log-exp
3×flip3-+ associate-*l* flip-+ unswap-sqr
2×pow1/3 sqrt-div associate-*r/
1×sub-neg flip3-- diff-log pow-prod-down prod-exp *-commutative flip-- cbrt-unprod
Counts
4 → 66
Calls
4 calls:
8.0ms
(* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im)))))
10.0ms
(- (* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im))))) re)
4.0ms
(cbrt (+ (* re re) (* im im)))
4.0ms
(cbrt (+ (* re re) (* im im)))

series365.0ms

Counts
4 → 12
Calls
4 calls:
105.0ms
(* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im)))))
79.0ms
(- (* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im))))) re)
89.0ms
(cbrt (+ (* re re) (* im im)))
92.0ms
(cbrt (+ (* re re) (* im im)))

simplify144.0ms

Algorithm
egg-herbie
Counts
78 → 78
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
0307930
11159870
24797842
35002842

prune281.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 18.4b

localize19.0ms

Local error

Found 4 expressions with local error:

31.6b
(cbrt (+ (* re re) (* im im)))
31.6b
(cbrt (+ (* re re) (* im im)))
31.6b
(cbrt (+ (* re re) (* im im)))
31.6b
(cbrt (+ (* re re) (* im im)))

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
12×cbrt-prod
8×add-sqr-sqrt add-cube-cbrt cbrt-div *-un-lft-identity
4×pow1 add-exp-log flip3-+ pow1/3 add-cbrt-cube flip-+ add-log-exp
Counts
4 → 52
Calls
4 calls:
4.0ms
(cbrt (+ (* re re) (* im im)))
4.0ms
(cbrt (+ (* re re) (* im im)))
4.0ms
(cbrt (+ (* re re) (* im im)))
4.0ms
(cbrt (+ (* re re) (* im im)))

series361.0ms

Counts
4 → 12
Calls
4 calls:
90.0ms
(cbrt (+ (* re re) (* im im)))
91.0ms
(cbrt (+ (* re re) (* im im)))
90.0ms
(cbrt (+ (* re re) (* im im)))
91.0ms
(cbrt (+ (* re re) (* im im)))

simplify51.0ms

Algorithm
egg-herbie
Counts
64 → 64
Iterations

Useful iterations: 2 (12.0ms)

IterNodesCost
0123488
1408452
21386444
35001444

prune358.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 18.4b

localize26.0ms

Local error

Found 4 expressions with local error:

31.6b
(cbrt (+ (* re re) (* im im)))
31.6b
(cbrt (+ (* re re) (* im im)))
31.6b
(cbrt (+ (* re re) (* im im)))
31.6b
(cbrt (+ (* re re) (* im im)))

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
12×cbrt-prod
8×add-sqr-sqrt add-cube-cbrt cbrt-div *-un-lft-identity
4×pow1 add-exp-log flip3-+ pow1/3 add-cbrt-cube flip-+ add-log-exp
Counts
4 → 52
Calls
4 calls:
4.0ms
(cbrt (+ (* re re) (* im im)))
4.0ms
(cbrt (+ (* re re) (* im im)))
4.0ms
(cbrt (+ (* re re) (* im im)))
4.0ms
(cbrt (+ (* re re) (* im im)))

series369.0ms

Counts
4 → 12
Calls
4 calls:
93.0ms
(cbrt (+ (* re re) (* im im)))
94.0ms
(cbrt (+ (* re re) (* im im)))
90.0ms
(cbrt (+ (* re re) (* im im)))
92.0ms
(cbrt (+ (* re re) (* im im)))

simplify50.0ms

Algorithm
egg-herbie
Counts
64 → 64
Iterations

Useful iterations: 2 (12.0ms)

IterNodesCost
0123488
1408452
21386444
35001444

prune407.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 18.4b

regimes176.0ms

Accuracy

32.9% (14.1b remaining)

Error of 31.7b against oracle of 17.6b and baseline of 38.6b

bsearch218.0ms

Steps
ItersRangePoint
9
1.9608280636258358e+114
2.747211200278764e+119
2.98053558728124e+118
4
2.1678204836809376e-60
3.3511168341522894e-60
2.19133113958617e-60
4
6.147769418428382e-71
1.1523539701310754e-70
1.1321272697325898e-70
10
-1.6329142053457655e-288
-1.2884785001595042e-303
-4.0771067353042325e-295
11
-7.101474352920752e-128
-3.5343660131329102e-152
-2.5585399092543814e-148

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06465
16465

end0.0ms

sample660.0ms

Algorithm
intervals
Results
204.0ms6089×body80valid
126.0ms656×body2560valid
72.0ms287×body5120valid
70.0ms460×body1280valid
32.0ms266×body640valid
14.0ms159×body320valid
5.0ms83×body160valid