Details

Time bar (total: 5.3s)

sample30.0ms

Algorithm
intervals
Results
8.0ms196×body80valid
4.0ms19×body2560valid
3.0ms17×body1280valid
2.0ms7×body5120valid
2.0ms12×body640valid
1.0ms5×body320valid

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: 35.3b

localize14.0ms

Local error

Found 2 expressions with local error:

0.0b
(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
27.1b
(sqrt (+ (* re re) (* im im)))

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
6×pow1
4×add-sqr-sqrt sqrt-div sqrt-prod
3×add-cube-cbrt *-un-lft-identity sqrt-pow1
2×add-exp-log pow1/2 associate-*r/ add-cbrt-cube add-log-exp
1×rem-sqrt-square flip3-- flip3-+ pow-prod-down flip-- flip-+
Counts
2 → 28
Calls
2 calls:
25.0ms
(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
8.0ms
(sqrt (+ (* re re) (* im im)))

series191.0ms

Counts
2 → 6
Calls
2 calls:
154.0ms
(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
37.0ms
(sqrt (+ (* re re) (* im im)))

simplify73.0ms

Algorithm
egg-herbie
Counts
34 → 34
Iterations

Useful iterations: 3 (68.0ms)

IterNodesCost
0212251
1732237
22378231
35002230

prune201.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 20.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
6.3b
(- (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
27.1b
(sqrt (+ (* re re) (* im im)))
27.1b
(sqrt (+ (* re re) (* im im)))

rewrite110.0ms

Algorithm
rewrite-expression-head
Rules
72×sqrt-prod
51×add-sqr-sqrt
34×sqrt-pow1
29×pow1
28×sqrt-div
18×add-cube-cbrt *-un-lft-identity pow1/2
15×swap-sqr
9×associate-*r* associate-*l* pow-prod-up unswap-sqr
8×flip3-+ flip-+
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×pow2 sub-neg flip3-- pow-plus sqrt-unprod diff-log prod-exp rem-square-sqrt *-commutative flip-- cbrt-unprod difference-of-squares
Counts
4 → 126
Calls
4 calls:
51.0ms
(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
39.0ms
(- (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
7.0ms
(sqrt (+ (* re re) (* im im)))
7.0ms
(sqrt (+ (* re re) (* im im)))

series144.0ms

Counts
4 → 12
Calls
4 calls:
35.0ms
(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
42.0ms
(- (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
35.0ms
(sqrt (+ (* re re) (* im im)))
33.0ms
(sqrt (+ (* re re) (* im im)))

simplify47.0ms

Algorithm
egg-herbie
Counts
138 → 138
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
02611112
1935975
25001951

prune537.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 15.8b

localize22.0ms

Local error

Found 4 expressions with local error:

27.1b
(sqrt (+ (* re re) (* im im)))
28.0b
(cbrt (+ (* re re) (* im im)))
28.0b
(cbrt (+ (* re re) (* im im)))
28.0b
(cbrt (+ (* re re) (* im im)))

rewrite26.0ms

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:
7.0ms
(sqrt (+ (* re re) (* im im)))
8.0ms
(cbrt (+ (* re re) (* im im)))
5.0ms
(cbrt (+ (* re re) (* im im)))
5.0ms
(cbrt (+ (* re re) (* im im)))

series298.0ms

Counts
4 → 12
Calls
4 calls:
32.0ms
(sqrt (+ (* re re) (* im im)))
88.0ms
(cbrt (+ (* re re) (* im im)))
88.0ms
(cbrt (+ (* re re) (* im im)))
91.0ms
(cbrt (+ (* re re) (* im im)))

simplify53.0ms

Algorithm
egg-herbie
Counts
66 → 66
Iterations

Useful iterations: 3 (47.0ms)

IterNodesCost
0141466
1440436
21469430
35002429

prune882.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 15.8b

localize18.0ms

Local error

Found 4 expressions with local error:

27.1b
(sqrt (+ (* re re) (* im im)))
27.1b
(sqrt (+ (* re re) (* im im)))
27.1b
(sqrt (+ (* re re) (* im im)))
27.1b
(sqrt (+ (* re re) (* im im)))

rewrite31.0ms

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:
7.0ms
(sqrt (+ (* re re) (* im im)))
7.0ms
(sqrt (+ (* re re) (* im im)))
8.0ms
(sqrt (+ (* re re) (* im im)))
8.0ms
(sqrt (+ (* re re) (* im im)))

series135.0ms

Counts
4 → 12
Calls
4 calls:
37.0ms
(sqrt (+ (* re re) (* im im)))
31.0ms
(sqrt (+ (* re re) (* im im)))
31.0ms
(sqrt (+ (* re re) (* im im)))
36.0ms
(sqrt (+ (* re re) (* im im)))

simplify141.0ms

Algorithm
egg-herbie
Counts
72 → 72
Iterations

Useful iterations: 5 (136.0ms)

IterNodesCost
089400
1215388
2503388
31265388
44227388
55002384

prune805.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 15.8b

regimes326.0ms

Accuracy

55.4% (9.3b remaining)

Error of 27.0b against oracle of 17.7b and baseline of 38.5b

bsearch313.0ms

Steps
ItersRangePoint
8
2.7734301821360193e+115
1.787425999150024e+119
2.8222969601602164e+115
8
2.1818278795648462e+74
1.5862851066486083e+77
1.5649349068796514e+77
7
-6.837641986712258e-308
5.371031682140196e-308
4.4035213685687e-311
8
-4.513417988214574e+66
-1.0332137592348076e+63
-6.708120304428754e+64

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06658
17058
27058

end0.0ms

sample807.0ms

Algorithm
intervals
Results
254.0ms6061×body80valid
176.0ms701×body2560valid
95.0ms489×body1280valid
82.0ms281×body5120valid
40.0ms262×body640valid
17.0ms128×body320valid
6.0ms78×body160valid