Details

Time bar (total: 6.5s)

sample43.0ms

Algorithm
intervals
Results
12.0ms198×body80valid
9.0ms24×body2560valid
4.0ms13×body1280valid
4.0ms9×body5120valid
2.0ms8×body640valid
1.0ms3×body320valid
0.0ms1×body160valid

simplify6.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0228
1248
2248

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.3b

localize12.0ms

Local error

Found 2 expressions with local error:

0.5b
(+ (sqrt (+ (* re re) (* im im))) re)
29.9b
(sqrt (+ (* re re) (* im im)))

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
5×*-un-lft-identity
4×add-sqr-sqrt add-log-exp
3×pow1 add-cube-cbrt sqrt-prod
2×add-exp-log flip3-+ sqrt-div add-cbrt-cube flip-+
1×+-commutative rem-sqrt-square sqrt-pow1 pow1/2 sum-log distribute-lft-out
Counts
2 → 27
Calls
2 calls:
13.0ms
(+ (sqrt (+ (* re re) (* im im))) re)
3.0ms
(sqrt (+ (* re re) (* im im)))

series13.0ms

Counts
2 → 6
Calls
2 calls:
7.0ms
(+ (sqrt (+ (* re re) (* im im))) re)
6.0ms
(sqrt (+ (* re re) (* im im)))

simplify79.0ms

Algorithm
egg-herbie
Counts
33 → 33
Iterations

Useful iterations: 3 (28.0ms)

IterNodesCost
0141198
1358186
2866182
32557181
45001181

prune285.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 17.9b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im)))))
4.4b
(+ (* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im))))) re)
30.9b
(cbrt (+ (* re re) (* im im)))
30.9b
(cbrt (+ (* re re) (* im im)))

rewrite26.0ms

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
4×flip3-+ flip-+
3×associate-*l* unswap-sqr
2×pow1/3 sqrt-div associate-*r/
1×+-commutative pow-prod-down prod-exp sum-log *-commutative cbrt-unprod
Counts
4 → 65
Calls
4 calls:
14.0ms
(* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im)))))
6.0ms
(+ (* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im))))) re)
2.0ms
(cbrt (+ (* re re) (* im im)))
2.0ms
(cbrt (+ (* re re) (* im im)))

series101.0ms

Counts
4 → 12
Calls
4 calls:
35.0ms
(* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im)))))
28.0ms
(+ (* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im))))) re)
19.0ms
(cbrt (+ (* re re) (* im im)))
19.0ms
(cbrt (+ (* re re) (* im im)))

simplify42.0ms

Algorithm
egg-herbie
Counts
77 → 77
Iterations

Useful iterations: 2 (33.0ms)

IterNodesCost
0323928
11214868
25002841

prune956.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 17.9b

localize17.0ms

Local error

Found 4 expressions with local error:

4.4b
(+ (* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im))))) re)
4.6b
(exp (log (+ (* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im))))) re)))
30.9b
(cbrt (+ (* re re) (* im im)))
30.9b
(cbrt (+ (* re re) (* im im)))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
6×cbrt-prod add-log-exp
5×pow1
4×add-exp-log cbrt-div exp-prod flip3-+ add-cbrt-cube flip-+
3×log-prod exp-sum
2×log-div exp-diff pow1/3
1×+-commutative sum-log log-pow rem-exp-log
Counts
4 → 54
Calls
4 calls:
6.0ms
(+ (* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im))))) re)
10.0ms
(exp (log (+ (* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im))))) re)))
2.0ms
(cbrt (+ (* re re) (* im im)))
2.0ms
(cbrt (+ (* re re) (* im im)))

series97.0ms

Counts
4 → 12
Calls
4 calls:
30.0ms
(+ (* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im))))) re)
29.0ms
(exp (log (+ (* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im))))) re)))
19.0ms
(cbrt (+ (* re re) (* im im)))
19.0ms
(cbrt (+ (* re re) (* im im)))

simplify92.0ms

Algorithm
egg-herbie
Counts
66 → 66
Iterations

Useful iterations: 3 (84.0ms)

IterNodesCost
0295892
1998798
23188739
35001733

prune1.0s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 17.9b

localize27.0ms

Local error

Found 4 expressions with local error:

30.9b
(cbrt (+ (* re re) (* im im)))
30.9b
(cbrt (+ (* re re) (* im im)))
30.9b
(cbrt (+ (* re re) (* im im)))
30.9b
(cbrt (+ (* re re) (* im im)))

rewrite9.0ms

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:
2.0ms
(cbrt (+ (* re re) (* im im)))
2.0ms
(cbrt (+ (* re re) (* im im)))
2.0ms
(cbrt (+ (* re re) (* im im)))
2.0ms
(cbrt (+ (* re re) (* im im)))

series77.0ms

Counts
4 → 12
Calls
4 calls:
19.0ms
(cbrt (+ (* re re) (* im im)))
19.0ms
(cbrt (+ (* re re) (* im im)))
19.0ms
(cbrt (+ (* re re) (* im im)))
21.0ms
(cbrt (+ (* re re) (* im im)))

simplify51.0ms

Algorithm
egg-herbie
Counts
64 → 64
Iterations

Useful iterations: 2 (12.0ms)

IterNodesCost
0123488
1408452
21386444
35001444

prune1.9s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 17.9b

regimes421.0ms

Accuracy

58.7% (8.9b remaining)

Error of 26.8b against oracle of 17.9b and baseline of 39.5b

bsearch37.0ms

Steps
ItersRangePoint
9
3.7878992299232015e+133
1.2064922412751594e+141
1.7097317442318103e+134
5
-8.482171429905235e-305
-3.7894152148416054e-305
-3.8320737481419555e-305

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04029
14029

end0.0ms

sample1.2s

Algorithm
intervals
Results
372.0ms6005×body80valid
283.0ms735×body2560valid
149.0ms460×body1280valid
135.0ms296×body5120valid
70.0ms283×body640valid
26.0ms144×body320valid
9.0ms77×body160valid