Details

Time bar (total: 2.9s)

sample12.0ms

Algorithm
intervals
Results
5.0ms256×body80valid

simplify4.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
074
174

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.3b

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b
(+ (* re re) (* im im))
27.5b
(sqrt (+ (* re re) (* im im)))

rewrite7.0ms

Algorithm
rewrite-expression-head
Rules
4×add-sqr-sqrt add-log-exp
3×pow1 add-cube-cbrt *-un-lft-identity sqrt-prod
2×add-exp-log flip3-+ sqrt-div add-cbrt-cube flip-+
1×+-commutative rem-sqrt-square sqrt-pow1 pow1/2 sum-log
Counts
2 → 26
Calls
2 calls:
3.0ms
(+ (* re re) (* im im))
4.0ms
(sqrt (+ (* re re) (* im im)))

series65.0ms

Counts
2 → 6
Calls
2 calls:
27.0ms
(+ (* re re) (* im im))
38.0ms
(sqrt (+ (* re re) (* im im)))

simplify49.0ms

Algorithm
egg-herbie
Counts
32 → 32
Iterations

Useful iterations: 3 (46.0ms)

IterNodesCost
0125177
1530163
21540163
35001162

prune78.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 6.5b

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (sqrt (+ (* re re) (* im im))))
0.5b
(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
27.5b
(sqrt (+ (* re re) (* im im)))
27.5b
(sqrt (+ (* re re) (* im im)))

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
82×sqrt-prod
54×add-sqr-sqrt
38×sqrt-pow1
32×sqrt-div
31×pow1
20×add-cube-cbrt *-un-lft-identity pow1/2
15×swap-sqr
9×flip3-+ associate-*r* associate-*l* pow-prod-up flip-+ unswap-sqr
6×add-exp-log add-cbrt-cube
5×pow-prod-down pow-sqr
4×frac-times rem-sqrt-square add-log-exp
2×associate-*r/ associate-*l/
1×pow2 pow-plus sqrt-unprod prod-exp rem-square-sqrt *-commutative cbrt-unprod
Counts
4 → 134
Calls
4 calls:
4.0ms
(sqrt (sqrt (+ (* re re) (* im im))))
26.0ms
(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
3.0ms
(sqrt (+ (* re re) (* im im)))
4.0ms
(sqrt (+ (* re re) (* im im)))

series194.0ms

Counts
4 → 12
Calls
4 calls:
84.0ms
(sqrt (sqrt (+ (* re re) (* im im))))
39.0ms
(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
34.0ms
(sqrt (+ (* re re) (* im im)))
38.0ms
(sqrt (+ (* re re) (* im im)))

simplify44.0ms

Algorithm
egg-herbie
Counts
146 → 146
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
02511056
1951985
25002964

prune243.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 6.5b

localize10.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (sqrt (sqrt (sqrt (+ (* re re) (* im im))))) (sqrt (sqrt (sqrt (+ (* re re) (* im im))))))
27.5b
(sqrt (+ (* re re) (* im im)))
27.5b
(sqrt (+ (* re re) (* im im)))
27.5b
(sqrt (+ (* re re) (* im im)))

rewrite56.0ms

Algorithm
rewrite-expression-head
Rules
165×sqrt-prod
82×add-sqr-sqrt
75×sqrt-pow1
42×sqrt-div
38×pow1
27×pow1/2
24×swap-sqr
23×add-cube-cbrt *-un-lft-identity
16×unswap-sqr
13×pow-prod-up
12×associate-*r* associate-*l*
9×flip3-+ flip-+
7×pow-prod-down pow-sqr
6×add-exp-log add-cbrt-cube
4×frac-times add-log-exp
3×rem-sqrt-square
2×associate-*r/ associate-*l/
1×pow2 pow-plus sqrt-unprod prod-exp rem-square-sqrt *-commutative cbrt-unprod
Counts
4 → 158
Calls
4 calls:
37.0ms
(* (sqrt (sqrt (sqrt (+ (* re re) (* im im))))) (sqrt (sqrt (sqrt (+ (* re re) (* im im))))))
3.0ms
(sqrt (+ (* re re) (* im im)))
4.0ms
(sqrt (+ (* re re) (* im im)))
4.0ms
(sqrt (+ (* re re) (* im im)))

series197.0ms

Counts
4 → 12
Calls
4 calls:
87.0ms
(* (sqrt (sqrt (sqrt (+ (* re re) (* im im))))) (sqrt (sqrt (sqrt (+ (* re re) (* im im))))))
35.0ms
(sqrt (+ (* re re) (* im im)))
40.0ms
(sqrt (+ (* re re) (* im im)))
35.0ms
(sqrt (+ (* re re) (* im im)))

simplify51.0ms

Algorithm
egg-herbie
Counts
170 → 170
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
02911436
110811310
250021275

prune507.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 6.5b

localize20.0ms

Local error

Found 4 expressions with local error:

27.5b
(sqrt (+ (* re re) (* im im)))
27.5b
(sqrt (+ (* re re) (* im im)))
27.5b
(sqrt (+ (* re re) (* im im)))
27.5b
(sqrt (+ (* re re) (* im im)))

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt sqrt-prod
8×pow1 add-cube-cbrt *-un-lft-identity sqrt-div
4×add-exp-log rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 add-cbrt-cube flip-+ add-log-exp
Counts
4 → 60
Calls
4 calls:
3.0ms
(sqrt (+ (* re re) (* im im)))
3.0ms
(sqrt (+ (* re re) (* im im)))
3.0ms
(sqrt (+ (* re re) (* im im)))
4.0ms
(sqrt (+ (* re re) (* im im)))

series141.0ms

Counts
4 → 12
Calls
4 calls:
36.0ms
(sqrt (+ (* re re) (* im im)))
34.0ms
(sqrt (+ (* re re) (* im im)))
34.0ms
(sqrt (+ (* re re) (* im im)))
37.0ms
(sqrt (+ (* re re) (* im im)))

simplify135.0ms

Algorithm
egg-herbie
Counts
72 → 72
Iterations

Useful iterations: 5 (130.0ms)

IterNodesCost
089400
1215388
2503388
31265388
44227388
55002384

prune313.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 6.5b

regimes270.0ms

Accuracy

59.2% (9.7b remaining)

Error of 17.8b against oracle of 8.1b and baseline of 31.9b

bsearch93.0ms

Steps
ItersRangePoint
11
5.10808278574109e+145
3.366560557353129e+171
1.2142912145306137e+146
9
1.1741963849460375e-217
2.1903360009039515e-208
1.1600661433813666e-208
7
2.00818341296373e-296
3.449635196547704e-295
9.194803090293717e-296
7
-6.579287999353623e+83
-2.1130938932944453e+82
-6.485144449769119e+83

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0239
1239

end0.0ms

sample297.0ms

Algorithm
intervals
Results
175.0ms8000×body80valid