Details

Time bar (total: 3.0s)

sample28.0ms

Algorithm
intervals
Results
6.0ms192×body80valid
4.0ms21×body2560valid
3.0ms18×body1280valid
2.0ms8×body5120valid
1.0ms8×body640valid
1.0ms7×body320valid
0.0ms2×body160valid

simplify7.0ms

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: 41.4b

localize10.0ms

Local error

Found 3 expressions with local error:

0.1b
(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
0.6b
(- (sqrt (+ (* re re) (* im im))) re)
31.6b
(sqrt (+ (* re re) (* im im)))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
9×add-sqr-sqrt
7×pow1
6×*-un-lft-identity
5×sqrt-prod add-log-exp
4×add-cube-cbrt sqrt-div
3×add-exp-log sqrt-pow1 add-cbrt-cube
2×flip3-- pow1/2 associate-*r/ flip-- difference-of-squares
1×sub-neg rem-sqrt-square flip3-+ diff-log pow-prod-down flip-+ distribute-lft-out--
Counts
3 → 43
Calls
3 calls:
8.0ms
(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
7.0ms
(- (sqrt (+ (* re re) (* im im))) re)
6.0ms
(sqrt (+ (* re re) (* im im)))

series270.0ms

Counts
3 → 9
Calls
3 calls:
175.0ms
(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
46.0ms
(- (sqrt (+ (* re re) (* im im))) re)
49.0ms
(sqrt (+ (* re re) (* im im)))

simplify75.0ms

Algorithm
egg-herbie
Counts
52 → 52
Iterations

Useful iterations: 3 (69.0ms)

IterNodesCost
0232382
1768356
22506346
35001344

prune157.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 17.7b

localize13.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
7.4b
(- (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
31.6b
(sqrt (+ (* re re) (* im im)))
31.6b
(sqrt (+ (* re re) (* im im)))

rewrite46.0ms

Algorithm
rewrite-expression-head
Rules
72×sqrt-prod
51×add-sqr-sqrt
34×sqrt-pow1
29×pow1
28×sqrt-div
18×add-cube-cbrt *-un-lft-identity pow1/2
15×swap-sqr
9×associate-*r* associate-*l* pow-prod-up unswap-sqr
8×flip3-+ flip-+
6×add-exp-log add-cbrt-cube add-log-exp
5×pow-prod-down pow-sqr
4×frac-times
2×rem-sqrt-square associate-*r/ associate-*l/
1×pow2 sub-neg flip3-- pow-plus sqrt-unprod diff-log prod-exp rem-square-sqrt *-commutative flip-- cbrt-unprod difference-of-squares
Counts
4 → 126
Calls
4 calls:
18.0ms
(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
15.0ms
(- (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
4.0ms
(sqrt (+ (* re re) (* im im)))
4.0ms
(sqrt (+ (* re re) (* im im)))

series157.0ms

Counts
4 → 12
Calls
4 calls:
36.0ms
(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
49.0ms
(- (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
35.0ms
(sqrt (+ (* re re) (* im im)))
36.0ms
(sqrt (+ (* re re) (* im im)))

simplify47.0ms

Algorithm
egg-herbie
Counts
138 → 138
Iterations

Useful iterations: 2 (33.0ms)

IterNodesCost
02611112
1935975
25001951

prune294.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 17.7b

localize22.0ms

Local error

Found 4 expressions with local error:

12.8b
(- (* (* (cbrt (sqrt (sqrt (+ (* re re) (* im im))))) (cbrt (sqrt (sqrt (+ (* re re) (* im im)))))) (pow (cbrt (sqrt (sqrt (+ (* re re) (* im im))))) 4)) re)
31.6b
(sqrt (+ (* re re) (* im im)))
31.6b
(sqrt (+ (* re re) (* im im)))
31.6b
(sqrt (+ (* re re) (* im im)))

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
9×sqrt-prod
7×pow1 add-cube-cbrt *-un-lft-identity
6×sqrt-div add-log-exp
4×add-exp-log add-cbrt-cube
3×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+
1×sub-neg flip3-- diff-log flip--
Counts
4 → 57
Calls
4 calls:
24.0ms
(- (* (* (cbrt (sqrt (sqrt (+ (* re re) (* im im))))) (cbrt (sqrt (sqrt (+ (* re re) (* im im)))))) (pow (cbrt (sqrt (sqrt (+ (* re re) (* im im))))) 4)) re)
4.0ms
(sqrt (+ (* re re) (* im im)))
4.0ms
(sqrt (+ (* re re) (* im im)))
4.0ms
(sqrt (+ (* re re) (* im im)))

series163.0ms

Counts
4 → 12
Calls
4 calls:
52.0ms
(- (* (* (cbrt (sqrt (sqrt (+ (* re re) (* im im))))) (cbrt (sqrt (sqrt (+ (* re re) (* im im)))))) (pow (cbrt (sqrt (sqrt (+ (* re re) (* im im))))) 4)) re)
35.0ms
(sqrt (+ (* re re) (* im im)))
40.0ms
(sqrt (+ (* re re) (* im im)))
35.0ms
(sqrt (+ (* re re) (* im im)))

simplify56.0ms

Algorithm
egg-herbie
Counts
69 → 69
Iterations

Useful iterations: 3 (49.0ms)

IterNodesCost
0158715
1470629
21784577
35002573

prune300.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 17.7b

localize9.0ms

Local error

Found 1 expressions with local error:

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

rewrite5.0ms

Algorithm
rewrite-expression-head
Rules
4×pow1
2×sqrt-pow1 sqrt-div associate-*r/
1×add-exp-log add-sqr-sqrt add-cube-cbrt flip3-- *-un-lft-identity pow1/2 pow-prod-down sqrt-prod add-cbrt-cube flip-- add-log-exp
Counts
1 → 13
Calls
1 calls:
5.0ms
(sqrt (* 2.0 (- im re)))

series149.0ms

Counts
1 → 3
Calls
1 calls:
149.0ms
(sqrt (* 2.0 (- im re)))

simplify47.0ms

Algorithm
egg-herbie
Counts
16 → 16
Iterations

Useful iterations: 3 (44.0ms)

IterNodesCost
0135103
140390
2146379
3500276

prune38.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 17.7b

regimes149.0ms

Accuracy

54.6% (9.7b remaining)

Error of 27.3b against oracle of 17.5b and baseline of 39.0b

bsearch217.0ms

Steps
ItersRangePoint
8
2.1220162855519154e+232
9.8597313162195e+236
2.1596231037151348e+232
8
1.0067691769660572e+160
4.5146386827049324e+163
1.3228005539027653e+163
8
8.759955465341852e-197
9.415971551391981e-194
3.311222574554871e-196
8
4.592090908020972e-292
2.209994737107717e-288
1.8012497291896643e-291
6
-6.667724969208778e+44
-4.3606823432867463e+43
-6.5586381711852656e+44

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06139
16139

end0.0ms

sample686.0ms

Algorithm
intervals
Results
208.0ms5986×body80valid
140.0ms731×body2560valid
73.0ms466×body1280valid
70.0ms301×body5120valid
37.0ms282×body640valid
18.0ms150×body320valid
5.0ms84×body160valid