Details

Time bar (total: 3.4s)

sample26.0ms

Algorithm
intervals
Results
6.0ms192×body80valid
5.0ms24×body2560valid
3.0ms19×body1280valid
1.0ms11×body640valid
1.0ms5×body5120valid
0.0ms4×body320valid
0.0ms1×body160valid

simplify7.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0178
1248
2308
3358
4358

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.6b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* re re) (* im im))
0.0b
(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
0.5b
(- (sqrt (+ (* re re) (* im im))) re)
29.2b
(sqrt (+ (* re re) (* im im)))

rewrite39.0ms

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:
2.0ms
(+ (* re re) (* im im))
11.0ms
(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
18.0ms
(- (sqrt (+ (* re re) (* im im))) re)
6.0ms
(sqrt (+ (* re re) (* im im)))

series280.0ms

Counts
4 → 12
Calls
4 calls:
25.0ms
(+ (* re re) (* im im))
164.0ms
(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
43.0ms
(- (sqrt (+ (* re re) (* im im))) re)
47.0ms
(sqrt (+ (* re re) (* im im)))

simplify94.0ms

Algorithm
egg-herbie
Counts
66 → 66
Iterations

Useful iterations: 3 (85.0ms)

IterNodesCost
0258459
1938422
23098412
35001410

prune174.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 18.7b

localize14.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im)))))
5.1b
(- (* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im))))) re)
30.2b
(cbrt (+ (* re re) (* im im)))
30.2b
(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
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:
12.0ms
(* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im)))))
7.0ms
(- (* (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)))

series361.0ms

Counts
4 → 12
Calls
4 calls:
105.0ms
(* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im)))))
78.0ms
(- (* (fabs (cbrt (+ (* re re) (* im im)))) (sqrt (cbrt (+ (* re re) (* im im))))) re)
87.0ms
(cbrt (+ (* re re) (* im im)))
90.0ms
(cbrt (+ (* re re) (* im im)))

simplify142.0ms

Algorithm
egg-herbie
Counts
78 → 78
Iterations

Useful iterations: 2 (31.0ms)

IterNodesCost
0307930
11159870
24797842
35002842

prune261.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 18.7b

localize5.0ms

rewrite0.0ms

Algorithm
rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms

Counts
0 → 0

simplify2.0ms

Algorithm
egg-herbie
Counts
0 → 0
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
000

prune5.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 18.7b

localize14.0ms

Local error

Found 4 expressions with local error:

1.8b
(+ (sqrt (+ (* re re) (* im im))) re)
6.5b
(sqrt (* 2.0 (/ (pow im 2) (+ (sqrt (+ (* re re) (* im im))) re))))
21.5b
(/ (pow im 2) (+ (sqrt (+ (* re re) (* im im))) re))
29.2b
(sqrt (+ (* re re) (* im im)))

rewrite56.0ms

Algorithm
rewrite-expression-head
Rules
44×*-un-lft-identity
32×times-frac
25×add-sqr-sqrt
24×add-cube-cbrt
15×unpow-prod-down
10×distribute-lft-out
9×add-exp-log
8×pow1 associate-/l*
6×add-cbrt-cube add-log-exp
5×unpow2 sqr-pow
4×associate-/r* sqrt-prod
3×sqrt-pow1 flip3-+ sqrt-div div-exp flip-+
2×pow1/2 associate-/r/
1×cbrt-undiv +-commutative pow-to-exp rem-sqrt-square frac-2neg associate-*r/ pow-prod-down pow-exp clear-num sum-log div-inv
Counts
4 → 99
Calls
4 calls:
13.0ms
(+ (sqrt (+ (* re re) (* im im))) re)
13.0ms
(sqrt (* 2.0 (/ (pow im 2) (+ (sqrt (+ (* re re) (* im im))) re))))
21.0ms
(/ (pow im 2) (+ (sqrt (+ (* re re) (* im im))) re))
6.0ms
(sqrt (+ (* re re) (* im im)))

series333.0ms

Counts
4 → 12
Calls
4 calls:
43.0ms
(+ (sqrt (+ (* re re) (* im im))) re)
191.0ms
(sqrt (* 2.0 (/ (pow im 2) (+ (sqrt (+ (* re re) (* im im))) re))))
62.0ms
(/ (pow im 2) (+ (sqrt (+ (* re re) (* im im))) re))
37.0ms
(sqrt (+ (* re re) (* im im)))

simplify50.0ms

Algorithm
egg-herbie
Counts
111 → 111
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
04171078
11461985
25001978

prune261.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 8.1b

regimes189.0ms

Accuracy

42.2% (18.8b remaining)

Error of 25.5b against oracle of 6.7b and baseline of 39.2b

bsearch360.0ms

Steps
ItersRangePoint
7
2.9532459451765213e+138
4.989131466200188e+139
4.913522889015211e+139
7
9.739044821180595e+118
3.475160617912536e+120
9.901031096395063e+118
9
1.710560695972295e+65
1.0659718078425485e+73
5.9159114050755255e+72
9
4.088050234911823e-51
8.784213076784244e-45
4.1429610238548e-51
8
1.7802006390317204e-106
2.295581360372771e-102
2.247960755260109e-102
7
3.599959993217496e-225
2.6749766297337815e-223
1.613465243355143e-224
8
1.2605780682660474e-272
4.4558089668946025e-270
7.942397244706197e-271
10
-5.991532222681368e+46
-9.78963830731076e+36
-5.919120282594202e+46

simplify3.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
09771
110271
210371
310371

end0.0ms

sample685.0ms

Algorithm
intervals
Results
206.0ms5992×body80valid
135.0ms682×body2560valid
75.0ms486×body1280valid
71.0ms292×body5120valid
40.0ms304×body640valid
16.0ms174×body320valid
4.0ms70×body160valid