Details

Time bar (total: 15.0s)

sample66.0ms

Algorithm
intervals
Results
19.0ms189×body80valid
14.0ms20×body2560valid
10.0ms21×body1280valid
7.0ms10×body5120valid
6.0ms14×body640valid
0.0ms1×body320valid
0.0ms1×body160valid

simplify10.0ms

Counts
1 → 1
Iterations
IterNodes
324
224
122
012

prune23.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 40.7b

localize24.0ms

Local error

Found 3 expressions with local error:

0.0b
(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
0.3b
(+ (sqrt (+ (* re re) (* im im))) re)
31.6b
(sqrt (+ (* re re) (* im im)))

rewrite75.0ms

Algorithm
rewrite-expression-head
Rules
7×pow1
6×*-un-lft-identity
5×add-sqr-sqrt add-log-exp
4×sqrt-div add-cube-cbrt sqrt-prod
3×sqrt-pow1 flip3-+ add-cbrt-cube add-exp-log flip-+ insert-posit16
2×pow1/2 associate-*r/
1×+-commutative rem-sqrt-square sum-log pow-prod-down distribute-lft-out
Counts
3 → 43
Calls
3 calls:
37.0ms
(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
26.0ms
(+ (sqrt (+ (* re re) (* im im))) re)
12.0ms
(sqrt (+ (* re re) (* im im)))

series350.0ms

Counts
3 → 9
Calls
3 calls:
223.0ms
(sqrt (* 2.0 (+ (sqrt (+ (* re re) (* im im))) re)))
84.0ms
(+ (sqrt (+ (* re re) (* im im))) re)
42.0ms
(sqrt (+ (* re re) (* im im)))

simplify674.0ms

Counts
52 → 52
Iterations
IterNodes
32046
2680
1245
0102

prune564.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 17.5b

localize37.0ms

Local error

Found 4 expressions with local error:

18.2b
(sqrt (* (cbrt (+ (* re re) (* im im))) (cbrt (+ (* re re) (* im im)))))
32.7b
(cbrt (+ (* re re) (* im im)))
32.7b
(cbrt (+ (* re re) (* im im)))
32.7b
(cbrt (+ (* re re) (* im im)))

rewrite54.0ms

Algorithm
rewrite-expression-head
Rules
18×cbrt-div
12×pow1
9×cbrt-prod sqrt-pow1 flip3-+ pow1/3 flip-+
8×sqrt-div
7×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
4×frac-times add-cbrt-cube add-exp-log insert-posit16 add-log-exp
2×pow-prod-down associate-*l/ associate-*r/ pow-sqr pow-prod-up
1×pow2 rem-sqrt-square pow-plus pow1/2 sqrt-prod
Counts
4 → 70
Calls
4 calls:
29.0ms
(sqrt (* (cbrt (+ (* re re) (* im im))) (cbrt (+ (* re re) (* im im)))))
8.0ms
(cbrt (+ (* re re) (* im im)))
8.0ms
(cbrt (+ (* re re) (* im im)))
8.0ms
(cbrt (+ (* re re) (* im im)))

series510.0ms

Counts
4 → 12
Calls
4 calls:
112.0ms
(sqrt (* (cbrt (+ (* re re) (* im im))) (cbrt (+ (* re re) (* im im)))))
146.0ms
(cbrt (+ (* re re) (* im im)))
118.0ms
(cbrt (+ (* re re) (* im im)))
133.0ms
(cbrt (+ (* re re) (* im im)))

simplify1.2s

Counts
82 → 82
Iterations
IterNodes
42656
3995
2380
1178
098

prune1.3s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 17.5b

localize96.0ms

Local error

Found 4 expressions with local error:

31.6b
(sqrt (+ (* re re) (* im im)))
31.6b
(sqrt (+ (* re re) (* im im)))
32.7b
(cbrt (+ (* re re) (* im im)))
32.7b
(cbrt (+ (* re re) (* im im)))

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
8×*-un-lft-identity add-cube-cbrt
6×cbrt-prod pow1 sqrt-prod
4×cbrt-div flip3-+ add-cbrt-cube sqrt-div add-exp-log flip-+ insert-posit16 add-log-exp
2×rem-sqrt-square sqrt-pow1 pow1/2 pow1/3
Counts
4 → 60
Calls
4 calls:
6.0ms
(sqrt (+ (* re re) (* im im)))
6.0ms
(sqrt (+ (* re re) (* im im)))
5.0ms
(cbrt (+ (* re re) (* im im)))
8.0ms
(cbrt (+ (* re re) (* im im)))

series318.0ms

Counts
4 → 12
Calls
4 calls:
54.0ms
(sqrt (+ (* re re) (* im im)))
47.0ms
(sqrt (+ (* re re) (* im im)))
108.0ms
(cbrt (+ (* re re) (* im im)))
108.0ms
(cbrt (+ (* re re) (* im im)))

simplify1.2s

Counts
72 → 72
Iterations
IterNodes
42674
3956
2339
1142
067

prune1.4s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 17.5b

localize38.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (sqrt (* 2.0 (+ (* im im) 0))) (sqrt (- (sqrt (+ (* re re) (* im im))) re)))
0.9b
(- (sqrt (+ (* re re) (* im im))) re)
31.2b
(sqrt (* 2.0 (+ (* im im) 0)))
31.6b
(sqrt (+ (* re re) (* im im)))

rewrite120.0ms

Algorithm
rewrite-expression-head
Rules
50×add-sqr-sqrt sqrt-prod
37×*-un-lft-identity
36×times-frac
25×add-cube-cbrt
12×difference-of-squares
9×associate-/r*
8×pow1 sqrt-div
6×add-cbrt-cube add-exp-log distribute-lft-out-- add-log-exp
4×associate-*r/ insert-posit16 associate-/l*
3×sqrt-pow1 flip3-+ flip-+
2×flip3-- pow1/2 associate-/r/ flip-- associate-/l/
1×cbrt-undiv rem-sqrt-square sqrt-undiv clear-num sub-neg frac-2neg diff-log div-exp pow-prod-down div-inv
Counts
4 → 113
Calls
4 calls:
62.0ms
(/ (sqrt (* 2.0 (+ (* im im) 0))) (sqrt (- (sqrt (+ (* re re) (* im im))) re)))
41.0ms
(- (sqrt (+ (* re re) (* im im))) re)
7.0ms
(sqrt (* 2.0 (+ (* im im) 0)))
6.0ms
(sqrt (+ (* re re) (* im im)))

series435.0ms

Counts
4 → 12
Calls
4 calls:
228.0ms
(/ (sqrt (* 2.0 (+ (* im im) 0))) (sqrt (- (sqrt (+ (* re re) (* im im))) re)))
73.0ms
(- (sqrt (+ (* re re) (* im im))) re)
64.0ms
(sqrt (* 2.0 (+ (* im im) 0)))
69.0ms
(sqrt (+ (* re re) (* im im)))

simplify1.4s

Counts
125 → 125
Iterations
IterNodes
33360
21095
1450
0216

prune1.6s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 10.2b

regimes317.0ms

Accuracy

68.3% (8.8b remaining)

Error of 18.8b against oracle of 10.0b and baseline of 37.7b

bsearch333.0ms

Steps
ItersRangePoint
8
1.674331304137391e+80
9.448026055101687e+83
8.853592150803574e+83
8
-2.3452459005976665e-204
-3.8661403751356754e-208
-3.933782877011124e-208
10
-9.857583095580377e+159
-7.097741162392738e+142
-1.2805350559242801e+154

simplify31.0ms

Iterations
IterNodes
264
164
050

end0.0ms

sample2.9s

Algorithm
intervals
Results
785.0ms6062×body80valid
691.0ms450×body1280valid
556.0ms650×body2560valid
339.0ms312×body5120valid
207.0ms289×body640valid
83.0ms145×body320valid
22.0ms92×body160valid