Details

Time bar (total: 3.6s)

sample24.0ms

Algorithm
intervals
Results
6.0ms201×body80valid
5.0ms25×body2560valid
2.0ms7×body5120valid
2.0ms10×body1280valid
1.0ms10×body640valid
0.0ms2×body320valid
0.0ms1×body160valid

simplify5.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0228
1248
2248

prune3.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.8b

localize10.0ms

Local error

Found 3 expressions with local error:

0.2b
(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
0.3b
(+ (sqrt (+ (* re re) (* im im))) re)
31.8b
(sqrt (+ (* re re) (* im im)))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
7×pow1
6×*-un-lft-identity
5×add-sqr-sqrt add-log-exp
4×add-cube-cbrt sqrt-div sqrt-prod
3×add-exp-log sqrt-pow1 flip3-+ add-cbrt-cube flip-+
2×pow1/2 associate-*r/
1×+-commutative rem-sqrt-square pow-prod-down sum-log distribute-lft-out
Counts
3 → 40
Calls
3 calls:
7.0ms
(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
6.0ms
(+ (sqrt (+ (* re re) (* im im))) re)
4.0ms
(sqrt (+ (* re re) (* im im)))

series274.0ms

Counts
3 → 9
Calls
3 calls:
182.0ms
(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
48.0ms
(+ (sqrt (+ (* re re) (* im im))) re)
44.0ms
(sqrt (+ (* re re) (* im im)))

simplify68.0ms

Algorithm
egg-herbie
Counts
49 → 49
Iterations

Useful iterations: 3 (63.0ms)

IterNodesCost
0244351
1743325
22278315
35001312

prune149.0ms

Filtered
49 candidates to 42 candidates (85.7%)
Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 17.5b

localize14.0ms

Local error

Found 4 expressions with local error:

0.7b
(cbrt (+ (sqrt (+ (* re re) (* im im))) re))
31.8b
(sqrt (+ (* re re) (* im im)))
31.8b
(sqrt (+ (* re re) (* im im)))
31.8b
(sqrt (+ (* re re) (* im im)))

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
10×*-un-lft-identity
9×sqrt-prod
8×add-cube-cbrt
7×pow1
6×sqrt-div
4×add-exp-log cbrt-prod flip3-+ add-cbrt-cube flip-+ add-log-exp
3×rem-sqrt-square sqrt-pow1 pow1/2
2×cbrt-div
1×pow1/3 distribute-lft-out
Counts
4 → 59
Calls
4 calls:
7.0ms
(cbrt (+ (sqrt (+ (* re re) (* im im))) re))
4.0ms
(sqrt (+ (* re re) (* im im)))
4.0ms
(sqrt (+ (* re re) (* im im)))
4.0ms
(sqrt (+ (* re re) (* im im)))

series258.0ms

Counts
4 → 12
Calls
4 calls:
141.0ms
(cbrt (+ (sqrt (+ (* re re) (* im im))) re))
40.0ms
(sqrt (+ (* re re) (* im im)))
36.0ms
(sqrt (+ (* re re) (* im im)))
40.0ms
(sqrt (+ (* re re) (* im im)))

simplify61.0ms

Algorithm
egg-herbie
Counts
71 → 71
Iterations

Useful iterations: 3 (55.0ms)

IterNodesCost
0221484
1682471
22102468
35001463

prune266.0ms

Filtered
71 candidates to 60 candidates (84.5%)
Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 17.4b

localize11.0ms

Local error

Found 4 expressions with local error:

0.5b
(- (sqrt (+ (* re re) (* im im))) re)
4.4b
(sqrt (* 2.0 (/ (* im im) (- (sqrt (+ (* re re) (* im im))) re))))
23.5b
(/ (* im im) (- (sqrt (+ (* re re) (* im im))) re))
31.8b
(sqrt (+ (* re re) (* im im)))

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
13×*-un-lft-identity
9×add-exp-log add-cbrt-cube
8×pow1
7×add-cube-cbrt sqrt-prod
6×times-frac associate-/r* add-log-exp difference-of-squares
3×sqrt-pow1 sqrt-div distribute-lft-out--
2×cbrt-undiv flip3-- pow1/2 div-exp associate-/r/ flip--
1×sub-neg rem-sqrt-square frac-2neg flip3-+ diff-log associate-*r/ pow-prod-down prod-exp clear-num cbrt-unprod flip-+ div-inv associate-/l*
Counts
4 → 71
Calls
4 calls:
7.0ms
(- (sqrt (+ (* re re) (* im im))) re)
10.0ms
(sqrt (* 2.0 (/ (* im im) (- (sqrt (+ (* re re) (* im im))) re))))
10.0ms
(/ (* im im) (- (sqrt (+ (* re re) (* im im))) re))
4.0ms
(sqrt (+ (* re re) (* im im)))

series364.0ms

Counts
4 → 12
Calls
4 calls:
46.0ms
(- (sqrt (+ (* re re) (* im im))) re)
206.0ms
(sqrt (* 2.0 (/ (* im im) (- (sqrt (+ (* re re) (* im im))) re))))
76.0ms
(/ (* im im) (- (sqrt (+ (* re re) (* im im))) re))
36.0ms
(sqrt (+ (* re re) (* im im)))

simplify39.0ms

Algorithm
egg-herbie
Counts
83 → 83
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
0369696
11474620
25001611

prune218.0ms

Filtered
83 candidates to 64 candidates (77.1%)
Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 13.2b

localize14.0ms

Local error

Found 4 expressions with local error:

0.5b
(- (sqrt (+ (* re re) (* im im))) re)
4.4b
(sqrt (* 2.0 (* (/ im (sqrt (- (sqrt (+ (* re re) (* im im))) re))) (/ im (sqrt (- (sqrt (+ (* re re) (* im im))) re))))))
31.8b
(sqrt (+ (* re re) (* im im)))
31.8b
(sqrt (+ (* re re) (* im im)))

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
12×pow1 add-sqr-sqrt
8×*-un-lft-identity sqrt-prod
7×sqrt-div
6×add-cube-cbrt add-log-exp
5×sqrt-pow1
4×add-exp-log associate-*r/ add-cbrt-cube
3×pow1/2 pow-prod-down
2×rem-sqrt-square flip3-+ flip-+ difference-of-squares
1×frac-times sub-neg flip3-- diff-log associate-*l/ flip-- distribute-lft-out--
Counts
4 → 60
Calls
4 calls:
7.0ms
(- (sqrt (+ (* re re) (* im im))) re)
26.0ms
(sqrt (* 2.0 (* (/ im (sqrt (- (sqrt (+ (* re re) (* im im))) re))) (/ im (sqrt (- (sqrt (+ (* re re) (* im im))) re))))))
4.0ms
(sqrt (+ (* re re) (* im im)))
4.0ms
(sqrt (+ (* re re) (* im im)))

series325.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(- (sqrt (+ (* re re) (* im im))) re)
206.0ms
(sqrt (* 2.0 (* (/ im (sqrt (- (sqrt (+ (* re re) (* im im))) re))) (/ im (sqrt (- (sqrt (+ (* re re) (* im im))) re))))))
35.0ms
(sqrt (+ (* re re) (* im im)))
36.0ms
(sqrt (+ (* re re) (* im im)))

simplify88.0ms

Algorithm
egg-herbie
Counts
72 → 72
Iterations

Useful iterations: 3 (81.0ms)

IterNodesCost
0294590
1979551
23232539
35001536

prune227.0ms

Filtered
72 candidates to 56 candidates (77.8%)
Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 11.1b

regimes363.0ms

Accuracy

66.4% (8.7b remaining)

Error of 19.9b against oracle of 11.2b and baseline of 37.1b

bsearch66.0ms

Steps
ItersRangePoint
9
1.3035143797826932e+113
1.0263498879426634e+121
1.9399661775247916e+118
3
9.650788373676541e-287
1.2576615377335737e-286
9.768996274967368e-287
2
-6.814808586201778e+164
-5.701746713112747e+164
-5.840879447248876e+164

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05330
15330

end0.0ms

sample668.0ms

Algorithm
intervals
Results
200.0ms6029×body80valid
136.0ms715×body2560valid
78.0ms471×body1280valid
64.0ms270×body5120valid
37.0ms281×body640valid
16.0ms151×body320valid
5.0ms83×body160valid