Details

Time bar (total: 4.2s)

sample28.0ms

Algorithm
intervals
Results
6.0ms184×body80valid
5.0ms28×body2560valid
3.0ms12×body5120valid
2.0ms12×body1280valid
1.0ms11×body320valid
1.0ms6×body640valid
0.0ms3×body160valid

simplify7.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0178
1248
2308
3358
4358

prune3.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 42.9b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* re re) (* im im))
0.3b
(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
1.0b
(- (sqrt (+ (* re re) (* im im))) re)
32.9b
(sqrt (+ (* re re) (* im im)))

rewrite26.0ms

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:
7.0ms
(+ (* re re) (* im im))
7.0ms
(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
7.0ms
(- (sqrt (+ (* re re) (* im im))) re)
4.0ms
(sqrt (+ (* re re) (* im im)))

series280.0ms

Counts
4 → 12
Calls
4 calls:
26.0ms
(+ (* re re) (* im im))
173.0ms
(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
45.0ms
(- (sqrt (+ (* re re) (* im im))) re)
36.0ms
(sqrt (+ (* re re) (* im im)))

simplify91.0ms

Algorithm
egg-herbie
Counts
66 → 66
Iterations

Useful iterations: 3 (85.0ms)

IterNodesCost
0258459
1938422
23098412
35001410

prune188.0ms

Filtered
66 candidates to 52 candidates (78.8%)
Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 20.9b

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re))) 3)
1.0b
(- (sqrt (+ (* re re) (* im im))) re)
18.7b
(cbrt (pow (sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re))) 3))
32.9b
(sqrt (+ (* re re) (* im im)))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt
14×cbrt-prod
13×*-un-lft-identity
11×add-cube-cbrt
9×pow1
8×unpow-prod-down cube-prod sqrt-prod
6×sqrt-div add-log-exp
5×add-exp-log add-cbrt-cube
4×cube-div pow-pow associate-*r/
3×pow-unpow flip3-- sqrt-pow1 flip--
2×cube-mult cbrt-div pow1/2 unpow3 difference-of-squares sqr-pow
1×pow-to-exp sub-neg rem-sqrt-square flip3-+ pow1/3 diff-log pow-prod-down pow-exp sqrt-pow2 rem-cbrt-cube flip-+ distribute-lft-out-- rem-cube-cbrt
Counts
4 → 86
Calls
4 calls:
10.0ms
(pow (sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re))) 3)
7.0ms
(- (sqrt (+ (* re re) (* im im))) re)
4.0ms
(cbrt (pow (sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re))) 3))
4.0ms
(sqrt (+ (* re re) (* im im)))

series707.0ms

Counts
4 → 12
Calls
4 calls:
456.0ms
(pow (sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re))) 3)
47.0ms
(- (sqrt (+ (* re re) (* im im))) re)
169.0ms
(cbrt (pow (sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re))) 3))
35.0ms
(sqrt (+ (* re re) (* im im)))

simplify57.0ms

Algorithm
egg-herbie
Counts
98 → 98
Iterations

Useful iterations: 2 (41.0ms)

IterNodesCost
0426918
11635878
25001860

prune251.0ms

Filtered
98 candidates to 64 candidates (65.3%)
Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 20.9b

localize16.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (sqrt (+ (* re re) (* im im))) re)
32.9b
(sqrt (+ (* re re) (* im im)))
32.9b
(sqrt (+ (* re re) (* im im)))
32.9b
(sqrt (+ (* re re) (* im im)))

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
10×sqrt-prod
9×*-un-lft-identity
7×pow1 add-cube-cbrt
6×sqrt-div add-log-exp
4×add-exp-log add-cbrt-cube
3×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+
2×difference-of-squares
1×sub-neg flip3-- diff-log flip-- distribute-lft-out--
Counts
4 → 60
Calls
4 calls:
7.0ms
(- (sqrt (+ (* re re) (* im im))) re)
4.0ms
(sqrt (+ (* re re) (* im im)))
4.0ms
(sqrt (+ (* re re) (* im im)))
4.0ms
(sqrt (+ (* re re) (* im im)))

series160.0ms

Counts
4 → 12
Calls
4 calls:
51.0ms
(- (sqrt (+ (* re re) (* im im))) re)
34.0ms
(sqrt (+ (* re re) (* im im)))
35.0ms
(sqrt (+ (* re re) (* im im)))
39.0ms
(sqrt (+ (* re re) (* im im)))

simplify85.0ms

Algorithm
egg-herbie
Counts
72 → 72
Iterations

Useful iterations: 4 (79.0ms)

IterNodesCost
0135422
1332410
2839406
32503405
45002402

prune292.0ms

Filtered
72 candidates to 58 candidates (80.6%)
Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 20.9b

localize15.0ms

Local error

Found 4 expressions with local error:

32.9b
(sqrt (* (* (cbrt (+ (* re re) (* im im))) (cbrt (+ (* re re) (* im im)))) (cbrt (+ (* re re) (* im im)))))
33.9b
(cbrt (+ (* re re) (* im im)))
33.9b
(cbrt (+ (* re re) (* im im)))
33.9b
(cbrt (+ (* re re) (* im im)))

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
60×cbrt-div
30×flip3-+ flip-+
28×frac-times
26×sqrt-div
24×pow1
15×sqrt-pow1
14×associate-*l/
12×pow1/3
9×cbrt-prod pow-prod-up
8×associate-*r/
7×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
6×pow-plus
5×pow-prod-down
4×add-exp-log add-cbrt-cube add-log-exp
3×pow-sqr
2×pow2
1×pow1/2 pow3 sqrt-prod
Counts
4 → 89
Calls
4 calls:
16.0ms
(sqrt (* (* (cbrt (+ (* re re) (* im im))) (cbrt (+ (* re re) (* im im)))) (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)))

series324.0ms

Counts
4 → 12
Calls
4 calls:
43.0ms
(sqrt (* (* (cbrt (+ (* re re) (* im im))) (cbrt (+ (* re re) (* im im)))) (cbrt (+ (* re re) (* im im)))))
92.0ms
(cbrt (+ (* re re) (* im im)))
93.0ms
(cbrt (+ (* re re) (* im im)))
96.0ms
(cbrt (+ (* re re) (* im im)))

simplify190.0ms

Algorithm
egg-herbie
Counts
101 → 101
Iterations

Useful iterations: 3 (176.0ms)

IterNodesCost
02871509
17091463
230771446
350011379

prune259.0ms

Filtered
101 candidates to 63 candidates (62.4%)
Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 20.9b

regimes405.0ms

Accuracy

56.6% (9.1b remaining)

Error of 27.4b against oracle of 18.3b and baseline of 39.3b

bsearch3.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04647
14647

end0.0ms

sample729.0ms

Algorithm
intervals
Results
209.0ms5946×body80valid
160.0ms753×body2560valid
81.0ms502×body1280valid
78.0ms293×body5120valid
36.0ms281×body640valid
14.0ms147×body320valid
5.0ms78×body160valid