Details

Time bar (total: 4.7s)

analyze516.0ms

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

sample45.0ms

Algorithm
intervals
Results
27.0ms256×body80valid
3.0ms31×body80nan

simplify4.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02316
12316

prune7.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 31.0b

Counts
2 → 1

localize24.0ms

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)))
0.6b
(* (log base) (log base))
28.6b
(sqrt (+ (* re re) (* im im)))

rewrite33.0ms

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:
7.0ms
(* (log (sqrt (+ (* re re) (* im im)))) (log base))
12.0ms
(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
6.0ms
(* (log base) (log base))
5.0ms
(sqrt (+ (* re re) (* im im)))

series83.0ms

Counts
4 → 12
Calls
4 calls:
25.0ms
(* (log (sqrt (+ (* re re) (* im im)))) (log base))
32.0ms
(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
18.0ms
(* (log base) (log base))
7.0ms
(sqrt (+ (* re re) (* im im)))

simplify67.0ms

Algorithm
egg-herbie
Counts
122 → 122
Iterations

Useful iterations: 2 (51.0ms)

IterNodesCost
04571398
117161276
250011225

prune280.0ms

Filtered
80 candidates to 122 candidates (-52.5%)
Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New10913122
Fresh000
Picked101
Done000
Total11013123

Merged error: 6.0b

Counts
123 → 13

localize23.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (sqrt (+ (* (log base) (log base)) (* 0.0 0.0))))
0.6b
(* (log base) (log base))
0.6b
(* (log base) (log base))
28.6b
(sqrt (+ (* re re) (* im im)))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
37×add-sqr-sqrt
36×*-un-lft-identity
32×add-cube-cbrt
31×pow1
18×times-frac
15×sqrt-prod
12×log-prod swap-sqr log-pow
10×add-exp-log add-cbrt-cube
8×associate-*r* associate-*l*
6×distribute-rgt-in distribute-lft-in associate-/r*
4×sqrt-div add-log-exp
3×flip3-+ flip-+ associate-/l*
2×pow2 pow-plus pow-prod-down prod-exp associate-/r/ pow-sqr *-commutative pow-prod-up cbrt-unprod associate-/l/ unswap-sqr
1×cbrt-undiv rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-exp clear-num div-inv
Counts
4 → 130
Calls
4 calls:
11.0ms
(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (sqrt (+ (* (log base) (log base)) (* 0.0 0.0))))
5.0ms
(* (log base) (log base))
5.0ms
(* (log base) (log base))
5.0ms
(sqrt (+ (* re re) (* im im)))

series48.0ms

Counts
4 → 12
Calls
4 calls:
13.0ms
(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (sqrt (+ (* (log base) (log base)) (* 0.0 0.0))))
15.0ms
(* (log base) (log base))
14.0ms
(* (log base) (log base))
6.0ms
(sqrt (+ (* re re) (* im im)))

simplify54.0ms

Algorithm
egg-herbie
Counts
142 → 142
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
03941641
113271515
250021483

prune256.0ms

Filtered
80 candidates to 142 candidates (-77.5%)
Pruning

15 alts after pruning (14 fresh and 1 done)

PrunedKeptTotal
New1375142
Fresh3912
Picked011
Done000
Total14015155

Merged error: 5.8b

Counts
155 → 15

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)) (+ (+ (* (log base) (* 2 (log (cbrt base)))) (* (log base) (log (cbrt base)))) (* 0.0 0.0)))
0.5b
(cbrt base)
0.5b
(cbrt base)
28.6b
(sqrt (+ (* re re) (* im im)))

rewrite20.0ms

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:
12.0ms
(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (+ (* (log base) (* 2 (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)))

series98.0ms

Counts
4 → 12
Calls
4 calls:
46.0ms
(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (+ (* (log base) (* 2 (log (cbrt base)))) (* (log base) (log (cbrt base)))) (* 0.0 0.0)))
21.0ms
(cbrt base)
24.0ms
(cbrt base)
6.0ms
(sqrt (+ (* re re) (* im im)))

simplify44.0ms

Algorithm
egg-herbie
Counts
80 → 80
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
03841340
112641221
250011183

prune184.0ms

Filtered
66 candidates to 80 candidates (-21.2%)
Pruning

17 alts after pruning (15 fresh and 2 done)

PrunedKeptTotal
New77380
Fresh11213
Picked011
Done011
Total781795

Merged error: 5.8b

Counts
95 → 17

localize20.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (+ (* (log base) (log base)) (* 0.0 0.0)) (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)))
0.4b
(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.6b
(* (log base) (log base))
28.6b
(sqrt (+ (* re re) (* im im)))

rewrite26.0ms

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:
9.0ms
(/ (+ (* (log base) (log base)) (* 0.0 0.0)) (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)))
6.0ms
(* (log (sqrt (+ (* re re) (* im im)))) (log base))
5.0ms
(* (log base) (log base))
4.0ms
(sqrt (+ (* re re) (* im im)))

series85.0ms

Counts
4 → 12
Calls
4 calls:
42.0ms
(/ (+ (* (log base) (log base)) (* 0.0 0.0)) (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)))
23.0ms
(* (log (sqrt (+ (* re re) (* im im)))) (log base))
14.0ms
(* (log base) (log base))
6.0ms
(sqrt (+ (* re re) (* im im)))

simplify57.0ms

Algorithm
egg-herbie
Counts
122 → 122
Iterations

Useful iterations: 2 (44.0ms)

IterNodesCost
04641397
117541281
250021229

prune135.0ms

Filtered
80 candidates to 122 candidates (-52.5%)
Pruning

17 alts after pruning (14 fresh and 3 done)

PrunedKeptTotal
New1193122
Fresh31114
Picked011
Done022
Total12217139

Merged error: 5.7b

Counts
139 → 17

regimes602.0ms

Accuracy

55.9% (11.1b remaining)

Error of 17.6b against oracle of 6.5b and baseline of 31.7b

bsearch380.0ms

Steps
ItersRangePoint
6
1.3813798952225883e+116
5.909711163419256e+116
5.3349171140952535e+116
7
-2.106754700100233e+132
-9.945769849051474e+129
-1.9795650308626623e+130

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04839
14839

end0.0ms

analyze422.0ms

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
794.0ms8000×body80valid
91.0ms965×body80nan

Profiling

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