Details

Time bar (total: 7.2s)

sample64.0ms

Algorithm
intervals
Results
23.0ms256×body80valid
22.0ms268×body80nan

simplify4.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02316
12316

prune4.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 33.0b

Counts
2 → 1

localize23.0ms

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))
30.5b
(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))
10.0ms
(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
5.0ms
(* (log base) (log base))
4.0ms
(sqrt (+ (* re re) (* im im)))

series384.0ms

Counts
4 → 12
Calls
4 calls:
95.0ms
(* (log (sqrt (+ (* re re) (* im im)))) (log base))
101.0ms
(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (log base) (log base)) (* 0.0 0.0)))
152.0ms
(* (log base) (log base))
36.0ms
(sqrt (+ (* re re) (* im im)))

simplify64.0ms

Algorithm
egg-herbie
Counts
122 → 122
Iterations

Useful iterations: 2 (47.0ms)

IterNodesCost
04451361
117511236
250021203

prune456.0ms

Filtered
122 candidates to 84 candidates (68.9%)
Pruning

14 alts after pruning (14 fresh and 0 done)

PrunedKeptTotal
New10814122
Fresh000
Picked101
Done000
Total10914123

Merged error: 8.0b

Counts
123 → 14

localize21.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (log (sqrt (+ (* re re) (* im im)))) (log base))
0.5b
(* (log base) (log base))
0.5b
(* (log base) (log base))
30.5b
(sqrt (+ (* re re) (* im im)))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
36×pow1
28×add-sqr-sqrt
25×*-un-lft-identity
21×add-cube-cbrt
18×log-prod
16×log-pow
14×associate-*l*
12×swap-sqr associate-*r*
10×add-exp-log add-cbrt-cube
9×distribute-rgt-in distribute-lft-in
4×add-log-exp
3×pow-prod-down prod-exp sqrt-prod *-commutative cbrt-unprod unswap-sqr
2×pow2 sqrt-pow1 pow-plus pow1/2 sqrt-div pow-sqr pow-prod-up
1×rem-sqrt-square flip3-+ flip-+
Counts
4 → 115
Calls
4 calls:
6.0ms
(* (log (sqrt (+ (* re re) (* im im)))) (log base))
5.0ms
(* (log base) (log base))
5.0ms
(* (log base) (log base))
4.0ms
(sqrt (+ (* re re) (* im im)))

series428.0ms

Counts
4 → 12
Calls
4 calls:
91.0ms
(* (log (sqrt (+ (* re re) (* im im)))) (log base))
144.0ms
(* (log base) (log base))
151.0ms
(* (log base) (log base))
41.0ms
(sqrt (+ (* re re) (* im im)))

simplify156.0ms

Algorithm
egg-herbie
Counts
127 → 127
Iterations

Useful iterations: 3 (143.0ms)

IterNodesCost
0262720
1966639
24724599
35001592

prune532.0ms

Filtered
127 candidates to 71 candidates (55.9%)
Pruning

16 alts after pruning (15 fresh and 1 done)

PrunedKeptTotal
New1252127
Fresh01313
Picked011
Done000
Total12516141

Merged error: 7.9b

Counts
141 → 16

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)))
0.6b
(cbrt base)
0.6b
(cbrt base)
30.5b
(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)))

series565.0ms

Counts
4 → 12
Calls
4 calls:
183.0ms
(/ (+ (* (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)))
170.0ms
(cbrt base)
175.0ms
(cbrt base)
36.0ms
(sqrt (+ (* re re) (* im im)))

simplify47.0ms

Algorithm
egg-herbie
Counts
80 → 80
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
03661306
112831187
250011169

prune423.0ms

Filtered
80 candidates to 67 candidates (83.8%)
Pruning

19 alts after pruning (17 fresh and 2 done)

PrunedKeptTotal
New77380
Fresh01414
Picked011
Done011
Total771996

Merged error: 7.9b

Counts
96 → 19

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)) (+ (* (neg (pow 0.0 3)) 0.0) (pow (log base) 4)))
0.5b
(* (log base) (log base))
0.9b
(pow (log base) 4)
30.5b
(sqrt (+ (* re re) (* im im)))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
24×add-sqr-sqrt
23×*-un-lft-identity
21×add-cube-cbrt
20×pow1
9×add-exp-log times-frac
8×add-cbrt-cube
7×log-pow
6×log-prod swap-sqr
4×unpow-prod-down associate-*r* associate-*l* add-log-exp
3×distribute-rgt-in pow-unpow distribute-lft-in flip3-+ associate-/r* sqrt-prod flip-+ associate-/l*
2×sqrt-div associate-/r/ associate-/l/
1×cbrt-undiv pow2 pow-to-exp rem-sqrt-square pow-pow frac-2neg sqrt-pow1 pow-plus pow1/2 div-exp pow-prod-down pow-exp prod-exp clear-num pow-sqr *-commutative pow-prod-up cbrt-unprod div-inv unswap-sqr sqr-pow
Counts
4 → 100
Calls
4 calls:
13.0ms
(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (neg (pow 0.0 3)) 0.0) (pow (log base) 4)))
5.0ms
(* (log base) (log base))
2.0ms
(pow (log base) 4)
4.0ms
(sqrt (+ (* re re) (* im im)))

series487.0ms

Counts
4 → 12
Calls
4 calls:
128.0ms
(/ (+ (* (log (sqrt (+ (* re re) (* im im)))) (log base)) (* (atan2 im re) 0.0)) (+ (* (neg (pow 0.0 3)) 0.0) (pow (log base) 4)))
154.0ms
(* (log base) (log base))
166.0ms
(pow (log base) 4)
39.0ms
(sqrt (+ (* re re) (* im im)))

simplify65.0ms

Algorithm
egg-herbie
Counts
112 → 112
Iterations

Useful iterations: 2 (53.0ms)

IterNodesCost
04651176
119401064
250021045

prune425.0ms

Filtered
112 candidates to 75 candidates (67.0%)
Pruning

20 alts after pruning (17 fresh and 3 done)

PrunedKeptTotal
New1084112
Fresh31316
Picked011
Done022
Total11120131

Merged error: 7.9b

Counts
131 → 20

regimes838.0ms

Accuracy

55.1% (10.9b remaining)

Error of 18.3b against oracle of 7.4b and baseline of 31.7b

bsearch319.0ms

Steps
ItersRangePoint
9
1.6149967553659361e+103
4.979531089514928e+111
2.9376780439363178e+109
7
1.1554162190448735e-166
3.6127672308085134e-165
1.1948525576789128e-166
10
-1.3401875567454295e-221
-1.9611360856757354e-231
-2.0294447150286705e-226
8
-1.0793712137777658e+77
-4.69191261873295e+73
-2.2437101586355944e+75

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
07076
17076

end0.0ms

sample1.8s

Algorithm
intervals
Results
713.0ms8000×body80valid
675.0ms8141×body80nan

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