Details

Time bar (total: 4.0s)

sample28.0ms

Algorithm
intervals
Results
6.0ms187×body80valid
4.0ms24×body1280valid
3.0ms15×body2560valid
2.0ms10×body5120valid
1.0ms10×body640valid
1.0ms8×body320valid
0.0ms2×body160valid

simplify8.0ms

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: 38.2b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* re re) (* im im))
1.0b
(- (sqrt (+ (* re re) (* im im))) re)
28.2b
(sqrt (+ (* re re) (* im im)))

rewrite57.0ms

Algorithm
rewrite-expression-head
Rules
9×add-sqr-sqrt
7×add-log-exp
6×*-un-lft-identity
4×pow1 add-cube-cbrt sqrt-prod
3×add-exp-log add-cbrt-cube
2×flip3-+ sqrt-div flip-+ difference-of-squares
1×+-commutative sub-neg rem-sqrt-square flip3-- sqrt-pow1 pow1/2 diff-log sum-log flip-- distribute-lft-out--
Counts
3 → 41
Calls
3 calls:
8.0ms
(+ (* re re) (* im im))
41.0ms
(- (sqrt (+ (* re re) (* im im))) re)
8.0ms
(sqrt (+ (* re re) (* im im)))

series115.0ms

Counts
3 → 9
Calls
3 calls:
28.0ms
(+ (* re re) (* im im))
50.0ms
(- (sqrt (+ (* re re) (* im im))) re)
37.0ms
(sqrt (+ (* re re) (* im im)))

simplify69.0ms

Algorithm
egg-herbie
Counts
50 → 50
Iterations

Useful iterations: 3 (64.0ms)

IterNodesCost
0172305
1661282
21936278
35002276

prune139.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 16.8b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* re re) (* im im))
5.7b
(exp (log (sqrt (+ (* re re) (* im im)))))
16.5b
(- (exp (log (sqrt (+ (* re re) (* im im))))) re)
28.2b
(sqrt (+ (* re re) (* im im)))

rewrite87.0ms

Algorithm
rewrite-expression-head
Rules
15×add-sqr-sqrt
10×*-un-lft-identity
8×add-cube-cbrt log-prod exp-sum add-log-exp
7×pow1 sqrt-prod
6×exp-prod
4×add-exp-log sqrt-div add-cbrt-cube
3×flip3-+ log-pow flip-+ difference-of-squares
2×log-div sqrt-pow1 pow1/2 exp-diff
1×+-commutative sub-neg rem-sqrt-square flip3-- diff-log sum-log flip-- rem-exp-log distribute-lft-out--
Counts
4 → 64
Calls
4 calls:
7.0ms
(+ (* re re) (* im im))
10.0ms
(exp (log (sqrt (+ (* re re) (* im im)))))
60.0ms
(- (exp (log (sqrt (+ (* re re) (* im im))))) re)
8.0ms
(sqrt (+ (* re re) (* im im)))

series153.0ms

Counts
4 → 12
Calls
4 calls:
28.0ms
(+ (* re re) (* im im))
39.0ms
(exp (log (sqrt (+ (* re re) (* im im)))))
48.0ms
(- (exp (log (sqrt (+ (* re re) (* im im))))) re)
39.0ms
(sqrt (+ (* re re) (* im im)))

simplify72.0ms

Algorithm
egg-herbie
Counts
76 → 76
Iterations

Useful iterations: 3 (66.0ms)

IterNodesCost
0223519
1737467
22078451
35001442

prune202.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 16.7b

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b
(+ (sqrt (+ (* re re) (* im im))) re)
4.7b
(sqrt (* 2.0 (/ (pow im 2) (+ (sqrt (+ (* re re) (* im im))) re))))
21.9b
(/ (pow im 2) (+ (sqrt (+ (* re re) (* im im))) re))
28.2b
(sqrt (+ (* re re) (* im im)))

rewrite108.0ms

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:
28.0ms
(+ (sqrt (+ (* re re) (* im im))) re)
26.0ms
(sqrt (* 2.0 (/ (pow im 2) (+ (sqrt (+ (* re re) (* im im))) re))))
44.0ms
(/ (pow im 2) (+ (sqrt (+ (* re re) (* im im))) re))
8.0ms
(sqrt (+ (* re re) (* im im)))

series354.0ms

Counts
4 → 12
Calls
4 calls:
51.0ms
(+ (sqrt (+ (* re re) (* im im))) re)
196.0ms
(sqrt (* 2.0 (/ (pow im 2) (+ (sqrt (+ (* re re) (* im im))) re))))
67.0ms
(/ (pow im 2) (+ (sqrt (+ (* re re) (* im im))) re))
40.0ms
(sqrt (+ (* re re) (* im im)))

simplify54.0ms

Algorithm
egg-herbie
Counts
111 → 111
Iterations

Useful iterations: 2 (44.0ms)

IterNodesCost
04171078
11461985
25001978

prune297.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 5.4b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (pow im (/ 2 2)) (/ (+ (sqrt (+ (* re re) (* im im))) re) im))
0.3b
(+ (sqrt (+ (* re re) (* im im))) re)
4.7b
(sqrt (* 2.0 (/ (pow im (/ 2 2)) (/ (+ (sqrt (+ (* re re) (* im im))) re) im))))
28.2b
(sqrt (+ (* re re) (* im im)))

rewrite122.0ms

Algorithm
rewrite-expression-head
Rules
208×times-frac
153×*-un-lft-identity
104×add-sqr-sqrt
103×add-cube-cbrt
51×unpow-prod-down
25×distribute-lft-out
17×add-exp-log sqr-pow
16×associate-/r*
9×div-exp add-cbrt-cube div-inv
8×pow1
7×associate-/l*
6×add-log-exp
4×sqrt-prod
3×cbrt-undiv sqrt-pow1 sqrt-div
2×pow-to-exp flip3-+ pow1/2 pow-exp flip-+
1×+-commutative rem-sqrt-square frac-2neg associate-*r/ pow-prod-down clear-num sum-log associate-/r/
Counts
4 → 193
Calls
4 calls:
46.0ms
(/ (pow im (/ 2 2)) (/ (+ (sqrt (+ (* re re) (* im im))) re) im))
28.0ms
(+ (sqrt (+ (* re re) (* im im))) re)
31.0ms
(sqrt (* 2.0 (/ (pow im (/ 2 2)) (/ (+ (sqrt (+ (* re re) (* im im))) re) im))))
8.0ms
(sqrt (+ (* re re) (* im im)))

series358.0ms

Counts
4 → 12
Calls
4 calls:
73.0ms
(/ (pow im (/ 2 2)) (/ (+ (sqrt (+ (* re re) (* im im))) re) im))
46.0ms
(+ (sqrt (+ (* re re) (* im im))) re)
197.0ms
(sqrt (* 2.0 (/ (pow im (/ 2 2)) (/ (+ (sqrt (+ (* re re) (* im im))) re) im))))
42.0ms
(sqrt (+ (* re re) (* im im)))

simplify138.0ms

Algorithm
egg-herbie
Counts
205 → 205
Iterations

Useful iterations: 1 (20.0ms)

IterNodesCost
07882657
136602402
250012402

prune377.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 2.8b

regimes323.0ms

Accuracy

45.6% (18.4b remaining)

Error of 22.6b against oracle of 4.2b and baseline of 38.0b

bsearch193.0ms

Steps
ItersRangePoint
8
1.1807101732312691e+142
5.3555028086657875e+144
5.301975457738901e+144
8
2.8505148529471227e-220
1.1324871769035144e-217
3.315327059634813e-219
8
-4.5513920484886933e-281
-4.293119643674365e-284
-2.3932815010602277e-282
6
-7.3832476150467864e-180
-8.505695752111334e-181
-8.861544571423392e-181
8
-3.72436965410306e+139
-1.0540944006331587e+136
-1.5057522058365376e+136

simplify3.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
08343
19643
29743
39743

end0.0ms

sample727.0ms

Algorithm
intervals
Results
209.0ms6046×body80valid
128.0ms661×body2560valid
81.0ms510×body1280valid
70.0ms300×body5120valid
41.0ms273×body640valid
13.0ms134×body320valid
5.0ms76×body160valid