Details

Time bar (total: 3.6s)

sample27.0ms

Algorithm
intervals
Results
6.0ms183×body80valid
4.0ms19×body2560valid
3.0ms22×body1280valid
3.0ms14×body5120valid
1.0ms11×body640valid
0.0ms4×body320valid
0.0ms3×body160valid

simplify5.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0228
1248
2248

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 43.1b

localize13.0ms

Local error

Found 2 expressions with local error:

0.5b
(+ (sqrt (+ (* re re) (* im im))) re)
32.1b
(sqrt (+ (* re re) (* im im)))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
5×*-un-lft-identity
4×add-sqr-sqrt add-log-exp
3×pow1 add-cube-cbrt sqrt-prod
2×add-exp-log flip3-+ sqrt-div add-cbrt-cube flip-+
1×+-commutative rem-sqrt-square sqrt-pow1 pow1/2 sum-log distribute-lft-out
Counts
2 → 27
Calls
2 calls:
14.0ms
(+ (sqrt (+ (* re re) (* im im))) re)
4.0ms
(sqrt (+ (* re re) (* im im)))

series84.0ms

Counts
2 → 6
Calls
2 calls:
47.0ms
(+ (sqrt (+ (* re re) (* im im))) re)
36.0ms
(sqrt (+ (* re re) (* im im)))

simplify81.0ms

Algorithm
egg-herbie
Counts
33 → 33
Iterations

Useful iterations: 3 (29.0ms)

IterNodesCost
0141198
1358186
2866182
32557181
45001181

prune121.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 17.2b

localize12.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
8.1b
(+ (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
32.1b
(sqrt (+ (* re re) (* im im)))
32.1b
(sqrt (+ (* re re) (* im im)))

rewrite56.0ms

Algorithm
rewrite-expression-head
Rules
72×sqrt-prod
50×add-sqr-sqrt
34×sqrt-pow1
29×pow1
28×sqrt-div
18×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 add-log-exp
5×pow-prod-down pow-sqr
4×frac-times
2×rem-sqrt-square associate-*r/ associate-*l/
1×+-commutative pow2 pow-plus sqrt-unprod prod-exp sum-log rem-square-sqrt *-commutative cbrt-unprod
Counts
4 → 124
Calls
4 calls:
27.0ms
(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
14.0ms
(+ (* (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)))

series156.0ms

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)))
37.0ms
(sqrt (+ (* re re) (* im im)))

simplify50.0ms

Algorithm
egg-herbie
Counts
136 → 136
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
02671096
1974974
25001950

prune308.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 17.2b

localize24.0ms

Local error

Found 4 expressions with local error:

32.1b
(sqrt (+ (* re re) (* im im)))
33.1b
(cbrt (+ (* re re) (* im im)))
33.1b
(cbrt (+ (* re re) (* im im)))
33.1b
(cbrt (+ (* re re) (* im im)))

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod add-sqr-sqrt
8×add-cube-cbrt *-un-lft-identity
6×cbrt-div
5×pow1
4×add-exp-log flip3-+ add-cbrt-cube flip-+ add-log-exp
3×pow1/3 sqrt-prod
2×sqrt-div
1×rem-sqrt-square sqrt-pow1 pow1/2
Counts
4 → 54
Calls
4 calls:
4.0ms
(sqrt (+ (* re re) (* im im)))
2.0ms
(cbrt (+ (* re re) (* im im)))
2.0ms
(cbrt (+ (* re re) (* im im)))
2.0ms
(cbrt (+ (* re re) (* im im)))

series322.0ms

Counts
4 → 12
Calls
4 calls:
35.0ms
(sqrt (+ (* re re) (* im im)))
96.0ms
(cbrt (+ (* re re) (* im im)))
96.0ms
(cbrt (+ (* re re) (* im im)))
95.0ms
(cbrt (+ (* re re) (* im im)))

simplify53.0ms

Algorithm
egg-herbie
Counts
66 → 66
Iterations

Useful iterations: 3 (48.0ms)

IterNodesCost
0141466
1440436
21469430
35002429

prune388.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 17.2b

localize24.0ms

Local error

Found 4 expressions with local error:

32.1b
(sqrt (+ (* re re) (* im im)))
32.1b
(sqrt (+ (* re re) (* im im)))
33.1b
(cbrt (+ (* re re) (* im im)))
33.1b
(cbrt (+ (* re re) (* im im)))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
8×add-cube-cbrt *-un-lft-identity
6×pow1 cbrt-prod sqrt-prod
4×add-exp-log cbrt-div flip3-+ sqrt-div add-cbrt-cube flip-+ add-log-exp
2×rem-sqrt-square sqrt-pow1 pow1/2 pow1/3
Counts
4 → 56
Calls
4 calls:
4.0ms
(sqrt (+ (* re re) (* im im)))
4.0ms
(sqrt (+ (* re re) (* im im)))
5.0ms
(cbrt (+ (* re re) (* im im)))
2.0ms
(cbrt (+ (* re re) (* im im)))

series271.0ms

Counts
4 → 12
Calls
4 calls:
42.0ms
(sqrt (+ (* re re) (* im im)))
36.0ms
(sqrt (+ (* re re) (* im im)))
96.0ms
(cbrt (+ (* re re) (* im im)))
98.0ms
(cbrt (+ (* re re) (* im im)))

simplify55.0ms

Algorithm
egg-herbie
Counts
68 → 68
Iterations

Useful iterations: 3 (49.0ms)

IterNodesCost
0141444
1440420
21469416
35002414

prune393.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 17.2b

regimes226.0ms

Accuracy

52.9% (10.1b remaining)

Error of 27.8b against oracle of 17.7b and baseline of 39.1b

bsearch166.0ms

Steps
ItersRangePoint
9
2.5638491307155068e+47
1.8078460056449616e+54
1.7737595496755384e+54
11
-1.697635983764772e-254
-9.078934504337964e-275
-1.2884729287301245e-263
8
-8.290788326405919e-112
-3.2816414843468158e-115
-5.480372687819121e-115

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06053
16053

end0.0ms

sample684.0ms

Algorithm
intervals
Results
197.0ms6023×body80valid
133.0ms653×body2560valid
80.0ms483×body1280valid
73.0ms309×body5120valid
41.0ms302×body640valid
13.0ms143×body320valid
5.0ms87×body160valid