Details

Time bar (total: 3.4s)

analyze494.0ms

Algorithm
search

sample22.0ms

Algorithm
intervals
Results
11.0ms256×body80valid
1.0ms16×body80invalid

simplify10.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0197
1367
2487
3667
4727
5727

prune4.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 24.5b

Counts
2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(- (* x.im y.re) (* x.re y.im))
0.0b
(+ (* y.re y.re) (* y.im y.im))
24.1b
(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
9×times-frac
7×add-log-exp
5×add-exp-log add-cbrt-cube
3×pow1 associate-/r* associate-/l*
2×flip3-- flip3-+ associate-/r/ flip-- flip-+ associate-/l/
1×cbrt-undiv +-commutative sub-neg frac-2neg diff-log div-sub div-exp clear-num sum-log div-inv
Counts
3 → 55
Calls
3 calls:
3.0ms
(- (* x.im y.re) (* x.re y.im))
4.0ms
(+ (* y.re y.re) (* y.im y.im))
8.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

series46.0ms

Counts
3 → 9
Calls
3 calls:
10.0ms
(- (* x.im y.re) (* x.re y.im))
5.0ms
(+ (* y.re y.re) (* y.im y.im))
30.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify38.0ms

Algorithm
egg-herbie
Counts
64 → 64
Iterations

Useful iterations: 2 (31.0ms)

IterNodesCost
0292541
11273493
25001491

prune99.0ms

Filtered
50 candidates to 64 candidates (-28.0%)
Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New57764
Fresh000
Picked101
Done000
Total58765

Merged error: 23.8b

Counts
65 → 7

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im)))) (sqrt (+ (* y.re y.re) (* y.im y.im))))
13.5b
(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
25.9b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
25.9b
(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite43.0ms

Algorithm
rewrite-expression-head
Rules
288×times-frac
164×add-sqr-sqrt
162×add-cube-cbrt *-un-lft-identity
156×sqrt-prod
27×associate-/l*
22×sqrt-div
18×associate-/r/
12×associate-/r*
11×add-exp-log flip3-+ add-cbrt-cube flip-+
9×div-inv
6×pow1
4×cbrt-undiv div-exp add-log-exp
3×div-sub associate-/l/
2×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 clear-num
1×flip3-- flip--
Counts
4 → 266
Calls
4 calls:
15.0ms
(/ (/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im)))) (sqrt (+ (* y.re y.re) (* y.im y.im))))
8.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
3.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
3.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

series77.0ms

Counts
4 → 12
Calls
4 calls:
27.0ms
(/ (/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im)))) (sqrt (+ (* y.re y.re) (* y.im y.im))))
38.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
6.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
6.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify90.0ms

Algorithm
egg-herbie
Counts
278 → 278
Iterations

Useful iterations: 2 (44.0ms)

IterNodesCost
07455703
128885224
250015172

prune180.0ms

Filtered
148 candidates to 278 candidates (-87.8%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New2744278
Fresh246
Picked011
Done000
Total2769285

Merged error: 20.8b

Counts
285 → 9

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (* (- (* x.im y.re) (* x.re y.im)) (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im))))) (sqrt (+ (* y.re y.re) (* y.im y.im))))
13.6b
(* (- (* x.im y.re) (* x.re y.im)) (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im)))))
25.9b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
25.9b
(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite43.0ms

Algorithm
rewrite-expression-head
Rules
38×add-sqr-sqrt
28×add-exp-log times-frac
26×*-un-lft-identity
24×add-cube-cbrt associate-*r*
23×sqrt-prod
18×add-cbrt-cube
9×div-exp
8×pow1 sqrt-div prod-exp
6×associate-/r* associate-/l/
5×cbrt-undiv unswap-sqr
4×frac-times flip3-- flip3-+ associate-*l/ associate-/r/ flip-- cbrt-unprod flip-+ add-log-exp
3×associate-*l*
2×rem-sqrt-square rec-exp sqrt-pow1 pow1/2 1-exp associate-*r/ un-div-inv div-inv
1×frac-2neg pow-prod-down clear-num *-commutative associate-/l*
Counts
4 → 122
Calls
4 calls:
16.0ms
(/ (* (- (* x.im y.re) (* x.re y.im)) (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im))))) (sqrt (+ (* y.re y.re) (* y.im y.im))))
15.0ms
(* (- (* x.im y.re) (* x.re y.im)) (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im)))))
3.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
3.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

series76.0ms

Counts
4 → 12
Calls
4 calls:
28.0ms
(/ (* (- (* x.im y.re) (* x.re y.im)) (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im))))) (sqrt (+ (* y.re y.re) (* y.im y.im))))
36.0ms
(* (- (* x.im y.re) (* x.re y.im)) (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im)))))
6.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
6.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify64.0ms

Algorithm
egg-herbie
Counts
134 → 134
Iterations

Useful iterations: 2 (48.0ms)

IterNodesCost
05071496
126341285
250011194

prune127.0ms

Filtered
88 candidates to 134 candidates (-52.3%)
Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New1340134
Fresh077
Picked011
Done011
Total1349143

Merged error: 20.8b

Counts
143 → 9

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im)))) (/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im)))))
13.5b
(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
25.9b
(sqrt (+ (* y.re y.re) (* y.im y.im)))
25.9b
(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite46.0ms

Algorithm
rewrite-expression-head
Rules
95×add-sqr-sqrt
76×times-frac
53×*-un-lft-identity
47×add-cube-cbrt sqrt-prod
28×add-exp-log
24×associate-*r* associate-*l*
18×add-cbrt-cube
15×unswap-sqr
10×sqrt-div
9×div-exp
8×pow1 prod-exp
6×associate-/r* associate-/r/
5×cbrt-undiv flip3-+ flip-+
4×cbrt-unprod add-log-exp
3×div-inv associate-/l*
2×rem-sqrt-square rec-exp sqrt-pow1 pow1/2 1-exp associate-/l/
1×frac-times flip3-- frac-2neg div-sub associate-*r/ pow-prod-down associate-*l/ clear-num *-commutative flip--
Counts
4 → 161
Calls
4 calls:
23.0ms
(* (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im)))) (/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im)))))
8.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
3.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
3.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

series74.0ms

Counts
4 → 12
Calls
4 calls:
27.0ms
(* (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im)))) (/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im)))))
35.0ms
(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
6.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))
6.0ms
(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify73.0ms

Algorithm
egg-herbie
Counts
173 → 173
Iterations

Useful iterations: 2 (50.0ms)

IterNodesCost
05822518
126382255
250012130

prune121.0ms

Filtered
113 candidates to 173 candidates (-53.1%)
Pruning

9 alts after pruning (6 fresh and 3 done)

PrunedKeptTotal
New1730173
Fresh066
Picked011
Done022
Total1739182

Merged error: 20.8b

Counts
182 → 9

regimes453.0ms

Accuracy

33.9% (2.1b remaining)

Error of 25.0b against oracle of 22.9b and baseline of 26.1b

bsearch1.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03133
13333
23333

end0.0ms

analyze551.0ms

Algorithm
search

sample559.0ms

Algorithm
intervals
Results
345.0ms8000×body80valid
18.0ms427×body80invalid

Profiling

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