Details

Time bar (total: 4.5s)

sample25.0ms

Algorithm
intervals
Results
6.0ms189×body80valid
4.0ms22×body2560valid
3.0ms12×body5120valid
2.0ms13×body1280valid
1.0ms11×body640valid
0.0ms5×body320valid
0.0ms4×body160valid

simplify6.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0228
1248
2248

prune3.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.0b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* re re) (* im im))
1.5b
(+ (sqrt (+ (* re re) (* im im))) re)
31.6b
(sqrt (+ (* re re) (* im im)))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
7×add-log-exp
6×*-un-lft-identity
5×add-sqr-sqrt
4×pow1 add-cube-cbrt
3×add-exp-log flip3-+ sqrt-prod add-cbrt-cube flip-+
2×+-commutative sqrt-div sum-log
1×rem-sqrt-square sqrt-pow1 pow1/2 distribute-lft-out
Counts
3 → 38
Calls
3 calls:
3.0ms
(+ (* re re) (* im im))
16.0ms
(+ (sqrt (+ (* re re) (* im im))) re)
3.0ms
(sqrt (+ (* re re) (* im im)))

series119.0ms

Counts
3 → 9
Calls
3 calls:
28.0ms
(+ (* re re) (* im im))
53.0ms
(+ (sqrt (+ (* re re) (* im im))) re)
38.0ms
(sqrt (+ (* re re) (* im im)))

simplify63.0ms

Algorithm
egg-herbie
Counts
47 → 47
Iterations

Useful iterations: 3 (58.0ms)

IterNodesCost
0178275
1689252
22017248
35001246

prune142.0ms

Filtered
47 candidates to 38 candidates (80.9%)
Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 17.5b

localize17.0ms

Local error

Found 4 expressions with local error:

0.6b
(- (sqrt (+ (* re re) (* im im))) re)
4.2b
(sqrt (* 2.0 (/ (pow im 2) (- (sqrt (+ (* re re) (* im im))) re))))
22.1b
(/ (pow im 2) (- (sqrt (+ (* re re) (* im im))) re))
31.6b
(sqrt (+ (* re re) (* im im)))

rewrite60.0ms

Algorithm
rewrite-expression-head
Rules
69×add-sqr-sqrt
48×*-un-lft-identity times-frac
28×add-cube-cbrt
21×unpow-prod-down
20×difference-of-squares
14×sqrt-prod
10×distribute-lft-out--
9×add-exp-log
8×pow1 associate-/l*
7×unpow2 sqr-pow
6×associate-/r* add-cbrt-cube add-log-exp
3×sqrt-pow1 sqrt-div div-exp
2×flip3-- pow1/2 associate-/r/ flip--
1×cbrt-undiv pow-to-exp sub-neg rem-sqrt-square frac-2neg flip3-+ diff-log associate-*r/ pow-prod-down pow-exp clear-num flip-+ div-inv
Counts
4 → 120
Calls
4 calls:
17.0ms
(- (sqrt (+ (* re re) (* im im))) re)
14.0ms
(sqrt (* 2.0 (/ (pow im 2) (- (sqrt (+ (* re re) (* im im))) re))))
21.0ms
(/ (pow im 2) (- (sqrt (+ (* re re) (* im im))) re))
4.0ms
(sqrt (+ (* re re) (* im im)))

series385.0ms

Counts
4 → 12
Calls
4 calls:
54.0ms
(- (sqrt (+ (* re re) (* im im))) re)
208.0ms
(sqrt (* 2.0 (/ (pow im 2) (- (sqrt (+ (* re re) (* im im))) re))))
80.0ms
(/ (pow im 2) (- (sqrt (+ (* re re) (* im im))) re))
42.0ms
(sqrt (+ (* re re) (* im im)))

simplify54.0ms

Algorithm
egg-herbie
Counts
132 → 132
Iterations

Useful iterations: 2 (39.0ms)

IterNodesCost
04471428
115821323
250011313

prune326.0ms

Filtered
132 candidates to 85 candidates (64.4%)
Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 13.6b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ im (/ (- (sqrt (+ (* re re) (* im im))) re) im))
0.6b
(- (sqrt (+ (* re re) (* im im))) re)
4.2b
(sqrt (* 2.0 (/ im (/ (- (sqrt (+ (* re re) (* im im))) re) im))))
31.6b
(sqrt (+ (* re re) (* im im)))

rewrite68.0ms

Algorithm
rewrite-expression-head
Rules
138×times-frac
121×add-sqr-sqrt
94×*-un-lft-identity
68×add-cube-cbrt
26×difference-of-squares
22×associate-/r*
17×sqrt-prod
13×distribute-lft-out--
9×add-exp-log add-cbrt-cube
8×pow1
6×add-log-exp
5×div-inv
3×cbrt-undiv sqrt-pow1 sqrt-div div-exp associate-/l*
2×pow1/2
1×sub-neg rem-sqrt-square flip3-- frac-2neg flip3-+ diff-log associate-*r/ pow-prod-down clear-num associate-/r/ flip-- flip-+
Counts
4 → 148
Calls
4 calls:
21.0ms
(/ im (/ (- (sqrt (+ (* re re) (* im im))) re) im))
18.0ms
(- (sqrt (+ (* re re) (* im im))) re)
19.0ms
(sqrt (* 2.0 (/ im (/ (- (sqrt (+ (* re re) (* im im))) re) im))))
4.0ms
(sqrt (+ (* re re) (* im im)))

series381.0ms

Counts
4 → 12
Calls
4 calls:
80.0ms
(/ im (/ (- (sqrt (+ (* re re) (* im im))) re) im))
48.0ms
(- (sqrt (+ (* re re) (* im im))) re)
209.0ms
(sqrt (* 2.0 (/ im (/ (- (sqrt (+ (* re re) (* im im))) re) im))))
43.0ms
(sqrt (+ (* re re) (* im im)))

simplify91.0ms

Algorithm
egg-herbie
Counts
160 → 160
Iterations

Useful iterations: 2 (67.0ms)

IterNodesCost
06501959
130451836
250011823

prune396.0ms

Filtered
160 candidates to 104 candidates (65.0%)
Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 10.6b

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 2.0 (/ im (/ (- im re) im)))
0.0b
(/ (- im re) im)
0.1b
(/ im (/ (- im re) im))
9.7b
(sqrt (* 2.0 (/ im (/ (- im re) im))))

rewrite69.0ms

Algorithm
rewrite-expression-head
Rules
237×times-frac
177×add-sqr-sqrt
168×*-un-lft-identity
118×add-cube-cbrt
62×associate-*r*
25×distribute-lft-out-- difference-of-squares
22×associate-/r*
20×add-exp-log add-cbrt-cube
10×div-inv
9×pow1
8×associate-/l*
7×cbrt-undiv div-exp
4×add-log-exp
3×associate-*l* prod-exp cbrt-unprod unswap-sqr
2×frac-2neg sqrt-pow1 associate-*r/ pow-prod-down clear-num associate-/r/ associate-/l/
1×flip3-- pow1/2 sqrt-div div-sub sqrt-prod *-commutative flip--
Counts
4 → 228
Calls
4 calls:
34.0ms
(* 2.0 (/ im (/ (- im re) im)))
7.0ms
(/ (- im re) im)
8.0ms
(/ im (/ (- im re) im))
8.0ms
(sqrt (* 2.0 (/ im (/ (- im re) im))))

series305.0ms

Counts
4 → 12
Calls
4 calls:
51.0ms
(* 2.0 (/ im (/ (- im re) im)))
38.0ms
(/ (- im re) im)
44.0ms
(/ im (/ (- im re) im))
171.0ms
(sqrt (* 2.0 (/ im (/ (- im re) im))))

simplify126.0ms

Algorithm
egg-herbie
Counts
240 → 240
Iterations

Useful iterations: 2 (102.0ms)

IterNodesCost
07421626
141581500
250011499

prune518.0ms

Filtered
240 candidates to 168 candidates (70.0%)
Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 10.6b

regimes375.0ms

Accuracy

52.8% (12.5b remaining)

Error of 24.7b against oracle of 12.3b and baseline of 38.7b

bsearch289.0ms

Steps
ItersRangePoint
5
1.3859668012923316e+39
5.407361050114019e+39
5.323647200381255e+39
6
1.2888602883193277e-191
1.0756529683068688e-190
3.931590104575209e-191
9
3.7751008726876715e-235
1.6016645181124128e-228
1.573305619337669e-228
9
-6.806283990879702e-262
-7.541756626495359e-267
-1.984730296439969e-262
4
-2.1257158676027876e-194
-1.276837797885082e-194
-1.448710066223221e-194
9
-9253.133766593879
-0.041603525395973645
-283.23902669347274
10
-1.0719231849388273e+91
-1.1809596141379282e+75
-4.3796494253210686e+83

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
08057
18057

end0.0ms

sample643.0ms

Algorithm
intervals
Results
198.0ms6044×body80valid
132.0ms715×body2560valid
80.0ms494×body1280valid
60.0ms263×body5120valid
31.0ms261×body640valid
13.0ms146×body320valid
5.0ms77×body160valid