Details

Time bar (total: 18.1s)

sample140.0ms

Algorithm
intervals
Results
16.0ms207×body80valid
10.0ms16×body2560valid
4.0ms8×body5120valid
3.0ms9×body1280valid
3.0ms11×body640valid
1.0ms5×body320valid

simplify118.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
01215
11715
22415
33015
43515
done3515

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.7b

localize36.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* re re) (* im im))
0.0b
(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
0.3b
(- (sqrt (+ (* re re) (* im im))) re)
30.9b
(sqrt (+ (* re re) (* im im)))

rewrite171.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
8×pow1 add-log-exp
7×*-un-lft-identity
5×add-cube-cbrt sqrt-prod
4×add-exp-log sqrt-div add-cbrt-cube
3×sqrt-pow1
2×flip3-- flip3-+ pow1/2 associate-*r/ flip-- flip-+ difference-of-squares
1×+-commutative sub-neg rem-sqrt-square diff-log pow-prod-down sum-log distribute-lft-out--
Counts
4 → 54
Calls
4 calls:
16.0ms
(+ (* re re) (* im im))
47.0ms
(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
86.0ms
(- (sqrt (+ (* re re) (* im im))) re)
18.0ms
(sqrt (+ (* re re) (* im im)))

series501.0ms

Counts
4 → 12
Calls
4 calls:
46.0ms
(+ (* re re) (* im im))
283.0ms
(sqrt (* 2.0 (- (sqrt (+ (* re re) (* im im))) re)))
91.0ms
(- (sqrt (+ (* re re) (* im im))) re)
80.0ms
(sqrt (+ (* re re) (* im im)))

simplify998.0ms

Counts
66 → 66
Iterations

Useful iterations: done (995.0ms)

IterNodesCost
0114942
1276836
21265752
done5000729

prune494.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 18.1b

localize57.0ms

Local error

Found 4 expressions with local error:

6.6b
(- (* (* (cbrt (sqrt (+ (* re re) (* im im)))) (cbrt (sqrt (+ (* re re) (* im im))))) (cbrt (sqrt (+ (* re re) (* im im))))) re)
30.9b
(sqrt (+ (* re re) (* im im)))
30.9b
(sqrt (+ (* re re) (* im im)))
30.9b
(sqrt (+ (* re re) (* im im)))

rewrite240.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
9×sqrt-prod
7×pow1 add-cube-cbrt *-un-lft-identity
6×sqrt-div add-log-exp
4×add-exp-log add-cbrt-cube
3×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+
1×sub-neg flip3-- diff-log flip--
Counts
4 → 57
Calls
4 calls:
195.0ms
(- (* (* (cbrt (sqrt (+ (* re re) (* im im)))) (cbrt (sqrt (+ (* re re) (* im im))))) (cbrt (sqrt (+ (* re re) (* im im))))) re)
14.0ms
(sqrt (+ (* re re) (* im im)))
14.0ms
(sqrt (+ (* re re) (* im im)))
15.0ms
(sqrt (+ (* re re) (* im im)))

series269.0ms

Counts
4 → 12
Calls
4 calls:
81.0ms
(- (* (* (cbrt (sqrt (+ (* re re) (* im im)))) (cbrt (sqrt (+ (* re re) (* im im))))) (cbrt (sqrt (+ (* re re) (* im im))))) re)
59.0ms
(sqrt (+ (* re re) (* im im)))
62.0ms
(sqrt (+ (* re re) (* im im)))
67.0ms
(sqrt (+ (* re re) (* im im)))

simplify1.3s

Counts
69 → 69
Iterations

Useful iterations: done (1.3s)

IterNodesCost
0641227
11501131
2398665
31455626
done5001618

prune585.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 18.1b

localize44.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (sqrt (* 2.0 (+ (* im im) 0))) (sqrt (+ (sqrt (+ (* re re) (* im im))) re)))
0.3b
(+ (sqrt (+ (* re re) (* im im))) re)
26.6b
(sqrt (* 2.0 (+ (* im im) 0)))
30.9b
(sqrt (+ (* re re) (* im im)))

rewrite199.0ms

Algorithm
rewrite-expression-head
Rules
35×*-un-lft-identity
32×sqrt-prod
28×times-frac
24×add-sqr-sqrt
23×add-cube-cbrt
8×pow1 sqrt-div
7×associate-/r*
6×add-exp-log add-cbrt-cube distribute-lft-out add-log-exp
5×flip3-+ flip-+
4×associate-*r/ associate-/l*
3×sqrt-pow1
2×pow1/2 associate-/r/ associate-/l/
1×cbrt-undiv +-commutative rem-sqrt-square sqrt-undiv frac-2neg div-exp pow-prod-down clear-num sum-log div-inv
Counts
4 → 96
Calls
4 calls:
90.0ms
(/ (sqrt (* 2.0 (+ (* im im) 0))) (sqrt (+ (sqrt (+ (* re re) (* im im))) re)))
57.0ms
(+ (sqrt (+ (* re re) (* im im))) re)
33.0ms
(sqrt (* 2.0 (+ (* im im) 0)))
15.0ms
(sqrt (+ (* re re) (* im im)))

series525.0ms

Counts
4 → 12
Calls
4 calls:
315.0ms
(/ (sqrt (* 2.0 (+ (* im im) 0))) (sqrt (+ (sqrt (+ (* re re) (* im im))) re)))
85.0ms
(+ (sqrt (+ (* re re) (* im im))) re)
64.0ms
(sqrt (* 2.0 (+ (* im im) 0)))
60.0ms
(sqrt (+ (* re re) (* im im)))

simplify1.6s

Counts
108 → 108
Iterations

Useful iterations: done (1.6s)

IterNodesCost
01982506
14622091
220731954
done50021936

prune809.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 13.6b

localize53.0ms

Local error

Found 4 expressions with local error:

0.3b
(+ (sqrt (+ (* re re) (* im im))) re)
0.3b
(* (sqrt 2.0) (/ (fabs im) (sqrt (+ (sqrt (+ (* re re) (* im im))) re))))
0.4b
(/ (fabs im) (sqrt (+ (sqrt (+ (* re re) (* im im))) re)))
30.9b
(sqrt (+ (* re re) (* im im)))

rewrite341.0ms

Algorithm
rewrite-expression-head
Rules
54×add-sqr-sqrt
53×*-un-lft-identity
46×times-frac
39×sqrt-prod
37×add-cube-cbrt
27×associate-*r*
11×add-exp-log add-cbrt-cube
8×distribute-lft-out
7×pow1 associate-/r*
6×sqrt-div associate-*l* add-log-exp unswap-sqr
4×flip3-+ associate-/r/ flip-+
3×associate-/l*
2×cbrt-undiv div-exp prod-exp cbrt-unprod div-inv
1×+-commutative rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 associate-*r/ pow-prod-down clear-num sum-log *-commutative
Counts
4 → 125
Calls
4 calls:
53.0ms
(+ (sqrt (+ (* re re) (* im im))) re)
193.0ms
(* (sqrt 2.0) (/ (fabs im) (sqrt (+ (sqrt (+ (* re re) (* im im))) re))))
72.0ms
(/ (fabs im) (sqrt (+ (sqrt (+ (* re re) (* im im))) re)))
15.0ms
(sqrt (+ (* re re) (* im im)))

series586.0ms

Counts
4 → 12
Calls
4 calls:
105.0ms
(+ (sqrt (+ (* re re) (* im im))) re)
260.0ms
(* (sqrt 2.0) (/ (fabs im) (sqrt (+ (sqrt (+ (* re re) (* im im))) re))))
163.0ms
(/ (fabs im) (sqrt (+ (sqrt (+ (* re re) (* im im))) re)))
59.0ms
(sqrt (+ (* re re) (* im im)))

simplify3.7s

Counts
137 → 137
Iterations

Useful iterations: done (3.7s)

IterNodesCost
02482920
16522642
240262470
done50002466

prune986.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 11.4b

regimes1.2s

Accuracy

67.6% (9.7b remaining)

Error of 17.5b against oracle of 7.7b and baseline of 37.8b

bsearch276.0ms

Steps
ItersRangePoint
8
1.8608651167086986e+124
1.5707892714413715e+127
2.5823924790830883e+125
8
-1.994112662543457e-258
-5.0272686634761357e-262
-5.091836382390402e-262
6
-9.002982014462326e+138
-9.457886154583405e+137
-6.439772273490177e+138

simplify12.0ms

Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
04071
15271
done5271

end0.0ms

sample2.9s

Algorithm
intervals
Results
775.0ms496×body1280valid
683.0ms6045×body80valid
454.0ms658×body2560valid
262.0ms270×body640valid
228.0ms291×body5120valid
42.0ms166×body320valid
12.0ms74×body160valid