Details

Time bar (total: 3.5s)

sample30.0ms

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

simplify9.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0198
1288
2368
3448
4468
5468

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.3b

localize10.0ms

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)))

rewrite64.0ms

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 expm1-log1p-u pow1/2 associate-*r/ add-cbrt-cube log1p-expm1-u add-log-exp
1×rem-sqrt-square flip3-- flip3-+ pow-prod-down flip-- flip-+ hypot-def
Counts
2 → 33
Calls
2 calls:
55.0ms
(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
8.0ms
(sqrt (+ (* re re) (* im im)))

series185.0ms

Counts
2 → 6
Calls
2 calls:
150.0ms
(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
35.0ms
(sqrt (+ (* re re) (* im im)))

simplify82.0ms

Algorithm
egg-herbie
Counts
39 → 39
Iterations

Useful iterations: 3 (75.0ms)

IterNodesCost
0230276
1819254
22736248
35002247

prune199.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 13.2b

localize9.0ms

Local error

Found 1 expressions with local error:

0.0b
(sqrt (* 2.0 (- (* 1 (hypot re im)) re)))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
4×pow1
2×sqrt-pow1 sqrt-div associate-*r/
1×add-exp-log add-sqr-sqrt expm1-log1p-u add-cube-cbrt flip3-- *-un-lft-identity pow1/2 pow-prod-down sqrt-prod add-cbrt-cube flip-- log1p-expm1-u add-log-exp
Counts
1 → 15
Calls
1 calls:
18.0ms
(sqrt (* 2.0 (- (* 1 (hypot re im)) re)))

series166.0ms

Counts
1 → 3
Calls
1 calls:
166.0ms
(sqrt (* 2.0 (- (* 1 (hypot re im)) re)))

simplify67.0ms

Algorithm
egg-herbie
Counts
18 → 18
Iterations

Useful iterations: 2 (16.0ms)

IterNodesCost
0164132
1504120
22179114
35001114

prune106.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 13.2b

localize10.0ms

Local error

Found 1 expressions with local error:

0.4b
(* (sqrt 2.0) (sqrt (- (* 1 (hypot re im)) re)))

rewrite36.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt
11×sqrt-prod
7×associate-*r*
6×*-un-lft-identity associate-*l*
5×pow1 add-cube-cbrt
4×unswap-sqr
3×add-exp-log pow-prod-down add-cbrt-cube
2×sqrt-pow1 pow1/2 sqrt-div associate-*r/
1×expm1-log1p-u flip3-- sqrt-unprod prod-exp *-commutative flip-- cbrt-unprod log1p-expm1-u distribute-lft-out-- add-log-exp
Counts
1 → 35
Calls
1 calls:
35.0ms
(* (sqrt 2.0) (sqrt (- (* 1 (hypot re im)) re)))

series170.0ms

Counts
1 → 3
Calls
1 calls:
169.0ms
(* (sqrt 2.0) (sqrt (- (* 1 (hypot re im)) re)))

simplify105.0ms

Algorithm
egg-herbie
Counts
38 → 38
Iterations

Useful iterations: 2 (23.0ms)

IterNodesCost
0205304
1761284
23905278
35001278

prune155.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 13.2b

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)))

rewrite114.0ms

Algorithm
rewrite-expression-head
Rules
72×sqrt-prod
52×add-sqr-sqrt
34×sqrt-pow1
29×pow1
28×sqrt-div
19×add-cube-cbrt *-un-lft-identity
18×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×expm1-log1p-u frac-times log1p-expm1-u
3×prod-diff
2×rem-sqrt-square associate-*r/ associate-*l/ hypot-def
1×pow2 sub-neg flip3-- pow-plus fma-neg sqrt-unprod diff-log prod-exp rem-square-sqrt *-commutative flip-- cbrt-unprod difference-of-squares
Counts
4 → 140
Calls
4 calls:
51.0ms
(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
40.0ms
(- (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
8.0ms
(sqrt (+ (* re re) (* im im)))
8.0ms
(sqrt (+ (* re re) (* im im)))

series140.0ms

Counts
4 → 12
Calls
4 calls:
31.0ms
(* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im)))))
47.0ms
(- (* (sqrt (sqrt (+ (* re re) (* im im)))) (sqrt (sqrt (+ (* re re) (* im im))))) re)
31.0ms
(sqrt (+ (* re re) (* im im)))
32.0ms
(sqrt (+ (* re re) (* im im)))

simplify59.0ms

Algorithm
egg-herbie
Counts
152 → 152
Iterations

Useful iterations: 2 (46.0ms)

IterNodesCost
03151122
11313959
25001931

prune591.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 6.4b

regimes229.0ms

Accuracy

18.8% (4.7b remaining)

Error of 11.9b against oracle of 7.2b and baseline of 13.0b

bsearch145.0ms

Steps
ItersRangePoint
8
2.7734301821360193e+115
1.787425999150024e+119
1.684472493440548e+117
8
2.1818278795648462e+74
1.5862851066486083e+77
1.1265757021678831e+77
4
1.2861463606709647e-114
2.483388498659756e-114
2.4354079188722606e-114

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 1 (1.0ms)

IterNodesCost
03928
14814
25114
35114

end0.0ms

sample797.0ms

Algorithm
intervals
Results
253.0ms6061×body80valid
166.0ms701×body2560valid
96.0ms489×body1280valid
82.0ms281×body5120valid
42.0ms262×body640valid
14.0ms128×body320valid
6.0ms78×body160valid