Details

Time bar (total: 4.7s)

analyze433.0ms

Algorithm
search
Search
TrueOtherFalseIter
0%99.9%0.1%0
0%99.9%0.1%1
0%99.9%0.1%2
0%99.9%0.1%3
0%99.9%0.1%4
0%99.9%0.1%5
0%99.9%0.1%6
23.4%51.5%25.1%7
24.2%50.7%25.1%8
24.6%50.3%25.1%9
36.9%25.5%37.6%10
37.2%25.3%37.6%11
37.3%25.1%37.6%12
43.5%12.7%43.8%13
43.6%12.6%43.8%14

sample39.0ms

Algorithm
intervals
Results
24.0ms256×body80valid
3.0ms36×body80nan

simplify3.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02328
12328

prune4.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 28.7b

Counts
2 → 1

localize20.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.4b
(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
0.5b
(* (log base) (log base))
26.6b
(sqrt (+ (* re re) (* im im)))

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
28×add-sqr-sqrt
25×*-un-lft-identity
23×pow1 add-cube-cbrt
12×log-prod
10×add-exp-log associate-*l* log-pow add-cbrt-cube
9×times-frac
8×associate-*r*
6×distribute-rgt-in distribute-lft-in swap-sqr
4×add-log-exp
3×flip3-+ associate-/r* sqrt-prod flip-+ associate-/l*
2×sqrt-pow1 pow1/2 sqrt-div pow-prod-down prod-exp associate-/r/ *-commutative cbrt-unprod associate-/l/ unswap-sqr
1×cbrt-undiv pow2 rem-sqrt-square frac-2neg pow-plus div-exp clear-num pow-sqr pow-prod-up div-inv
Counts
4 → 110
Calls
4 calls:
6.0ms
(* (log (sqrt (+ (* re re) (* im im)))) (log base))
9.0ms
(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
4.0ms
(* (log base) (log base))
4.0ms
(sqrt (+ (* re re) (* im im)))

series68.0ms

Counts
4 → 12
Calls
4 calls:
21.0ms
(* (log (sqrt (+ (* re re) (* im im)))) (log base))
25.0ms
(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
15.0ms
(* (log base) (log base))
6.0ms
(sqrt (+ (* re re) (* im im)))

simplify53.0ms

Algorithm
egg-herbie
Counts
122 → 122
Iterations

Useful iterations: 0 (40.0ms)

IterNodesCost
054352029

prune270.0ms

Filtered
85 candidates to 122 candidates (-43.5%)
Pruning

17 alts after pruning (17 fresh and 0 done)

PrunedKeptTotal
New10517122
Fresh000
Picked101
Done000
Total10617123

Merged error: 6.9b

Counts
123 → 17

localize25.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.4b
(/ (+ (pow (log base) 2) (* 0.0 0.0)) (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)))
0.5b
(pow (log base) 2)
26.6b
(sqrt (+ (* re re) (* im im)))

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
22×add-sqr-sqrt
19×add-cube-cbrt *-un-lft-identity
12×pow1
9×add-exp-log times-frac
8×add-cbrt-cube
6×log-prod associate-*l*
5×log-pow
4×unpow-prod-down associate-*r* add-log-exp
3×distribute-rgt-in pow-unpow distribute-lft-in flip3-+ associate-/r* sqrt-prod flip-+ associate-/l*
2×sqrt-pow1 pow1/2 sqrt-div associate-/r/ associate-/l/
1×cbrt-undiv pow-to-exp rem-sqrt-square pow-pow frac-2neg div-exp pow-prod-down pow-exp prod-exp clear-num *-commutative cbrt-unprod div-inv unpow2 unswap-sqr sqr-pow
Counts
4 → 93
Calls
4 calls:
6.0ms
(* (log (sqrt (+ (* re re) (* im im)))) (log base))
9.0ms
(/ (+ (pow (log base) 2) (* 0.0 0.0)) (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)))
2.0ms
(pow (log base) 2)
4.0ms
(sqrt (+ (* re re) (* im im)))

series89.0ms

Counts
4 → 12
Calls
4 calls:
21.0ms
(* (log (sqrt (+ (* re re) (* im im)))) (log base))
47.0ms
(/ (+ (pow (log base) 2) (* 0.0 0.0)) (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)))
14.0ms
(pow (log base) 2)
6.0ms
(sqrt (+ (* re re) (* im im)))

simplify41.0ms

Algorithm
egg-herbie
Counts
105 → 105
Iterations

Useful iterations: 0 (29.0ms)

IterNodesCost
055271945

prune237.0ms

Filtered
78 candidates to 105 candidates (-34.6%)
Pruning

20 alts after pruning (19 fresh and 1 done)

PrunedKeptTotal
New1014105
Fresh11516
Picked011
Done000
Total10220122

Merged error: 6.9b

Counts
122 → 20

localize26.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (+ (* 2 (* (log base) (log (cbrt base)))) (* (log base) (log (cbrt base)))) (* 0.0 0.0)))
0.6b
(cbrt base)
0.6b
(cbrt base)
26.6b
(sqrt (+ (* re re) (* im im)))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt
15×add-cube-cbrt *-un-lft-identity
9×times-frac
6×add-exp-log cbrt-prod add-cbrt-cube
5×pow1
4×add-log-exp
3×flip3-+ associate-/r* sqrt-prod flip-+ associate-/l*
2×pow1/3 sqrt-div associate-/r/ associate-/l/
1×cbrt-undiv rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-exp clear-num div-inv
Counts
4 → 68
Calls
4 calls:
14.0ms
(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (+ (* 2 (* (log base) (log (cbrt base)))) (* (log base) (log (cbrt base)))) (* 0.0 0.0)))
1.0ms
(cbrt base)
1.0ms
(cbrt base)
4.0ms
(sqrt (+ (* re re) (* im im)))

series101.0ms

Counts
4 → 12
Calls
4 calls:
51.0ms
(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (+ (* 2 (* (log base) (log (cbrt base)))) (* (log base) (log (cbrt base)))) (* 0.0 0.0)))
22.0ms
(cbrt base)
22.0ms
(cbrt base)
6.0ms
(sqrt (+ (* re re) (* im im)))

simplify37.0ms

Algorithm
egg-herbie
Counts
80 → 80
Iterations

Useful iterations: 0 (26.0ms)

IterNodesCost
049411523
149411523

prune200.0ms

Filtered
64 candidates to 80 candidates (-25.0%)
Pruning

21 alts after pruning (20 fresh and 1 done)

PrunedKeptTotal
New76480
Fresh21618
Picked101
Done011
Total7921100

Merged error: 6.9b

Counts
100 → 21

localize35.0ms

Local error

Found 4 expressions with local error:

0.7b
(pow (* (log (sqrt (+ (* re re) (* im im)))) (log base)) 3)
26.6b
(sqrt (+ (* re re) (* im im)))
26.6b
(sqrt (+ (* re re) (* im im)))
26.6b
(sqrt (+ (* re re) (* im im)))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
10×pow1
9×sqrt-prod
8×add-cube-cbrt *-un-lft-identity
7×add-exp-log add-cbrt-cube
6×sqrt-div
4×add-log-exp
3×rem-sqrt-square pow-unpow sqrt-pow1 flip3-+ pow1/2 flip-+
2×pow-pow pow-exp rem-cube-cbrt
1×cube-mult pow-to-exp unpow-prod-down unpow3 cube-prod pow-prod-down prod-exp cbrt-unprod sqr-pow
Counts
4 → 67
Calls
4 calls:
5.0ms
(pow (* (log (sqrt (+ (* re re) (* im im)))) (log base)) 3)
4.0ms
(sqrt (+ (* re re) (* im im)))
4.0ms
(sqrt (+ (* re re) (* im im)))
4.0ms
(sqrt (+ (* re re) (* im im)))

series70.0ms

Counts
4 → 12
Calls
4 calls:
52.0ms
(pow (* (log (sqrt (+ (* re re) (* im im)))) (log base)) 3)
6.0ms
(sqrt (+ (* re re) (* im im)))
6.0ms
(sqrt (+ (* re re) (* im im)))
6.0ms
(sqrt (+ (* re re) (* im im)))

simplify35.0ms

Algorithm
egg-herbie
Counts
79 → 79
Iterations

Useful iterations: 0 (25.0ms)

IterNodesCost
05393810

prune171.0ms

Filtered
62 candidates to 79 candidates (-27.4%)
Pruning

22 alts after pruning (20 fresh and 2 done)

PrunedKeptTotal
New77279
Fresh11819
Picked011
Done011
Total7822100

Merged error: 6.8b

Counts
100 → 22

regimes840.0ms

Accuracy

56.8% (10.9b remaining)

Error of 17.8b against oracle of 6.9b and baseline of 32.1b

bsearch278.0ms

Steps
ItersRangePoint
8
3.876663909787781e+29
4.4016837821388e+33
3.5391957870912594e+32
2
-1.3596588596739808e+66
-1.1835879469196704e+66
-1.337649995579692e+66

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05376
15376

end0.0ms

analyze425.0ms

Algorithm
search
Search
TrueOtherFalseIter
0%99.9%0.1%0
0%99.9%0.1%1
0%99.9%0.1%2
0%99.9%0.1%3
0%99.9%0.1%4
0%99.9%0.1%5
0%99.9%0.1%6
23.4%51.5%25.1%7
24.2%50.7%25.1%8
24.6%50.3%25.1%9
36.9%25.5%37.6%10
37.2%25.3%37.6%11
37.3%25.1%37.6%12
43.5%12.7%43.8%13
43.6%12.6%43.8%14

sample1.1s

Algorithm
intervals
Results
809.0ms8000×body80valid
93.0ms1018×body80nan

Profiling

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