Details

Time bar (total: 4.0s)

sample451.0ms

Algorithm
intervals
Results
70.0ms69×body1280valid
27.0ms256×body80valid
27.0ms50×body640valid
6.0ms17×body320valid
2.0ms1×body2560valid
1.0ms5×body160valid

simplify43.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 1 (4.0ms)

IterNodesCost
03121
15320
28420
320320
487920
5500120

prune17.0ms

Filtered
1 candidates to 1 candidates (100.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 33.5b

Counts
2 → 2

localize26.0ms

Local error

Found 4 expressions with local error:

1.3b
(* (atan2 x.im x.re) y.re)
29.3b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.3b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
34.0b
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
8×pow1 add-cube-cbrt *-un-lft-identity
6×add-exp-log sqrt-prod add-cbrt-cube
4×sqrt-div add-log-exp
3×associate-*r* associate-*l*
2×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+
1×sin-sum pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
4 → 56
Calls
4 calls:
4.0ms
(* (atan2 x.im x.re) y.re)
4.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
11.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
9.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series255.0ms

Counts
4 → 12
Calls
4 calls:
17.0ms
(* (atan2 x.im x.re) y.re)
37.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
39.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
162.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify76.0ms

Algorithm
egg-herbie
Counts
68 → 68
Iterations

Useful iterations: 2 (14.0ms)

IterNodesCost
0194425
1496388
21117386
32390386
45002386

prune332.0ms

Filtered
68 candidates to 54 candidates (79.4%)
Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New581068
Fresh011
Picked101
Done000
Total591170

Merged error: 18.4b

Counts
70 → 11

localize31.0ms

Local error

Found 4 expressions with local error:

29.3b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
34.0b
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
34.0b
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
34.0b
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
6×add-sqr-sqrt
5×pow1 add-cube-cbrt *-un-lft-identity
4×add-exp-log add-cbrt-cube add-log-exp
3×sin-sum sqrt-prod
2×sqrt-div
1×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+
Counts
4 → 39
Calls
4 calls:
4.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
7.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
7.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
7.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series485.0ms

Counts
4 → 12
Calls
4 calls:
40.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
148.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
149.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))
148.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify162.0ms

Algorithm
egg-herbie
Counts
51 → 51
Iterations

Useful iterations: 4 (54.0ms)

IterNodesCost
0142553
1288487
2611487
31512487
44748486
55001486

prune336.0ms

Filtered
51 candidates to 48 candidates (94.1%)
Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New50151
Fresh1910
Picked011
Done000
Total511162

Merged error: 18.4b

Counts
62 → 11

localize23.0ms

Local error

Found 4 expressions with local error:

1.3b
(* (atan2 x.im x.re) y.re)
29.3b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
29.3b
(sqrt (+ (* x.re x.re) (* x.im x.im)))
34.0b
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
8×pow1 add-cube-cbrt *-un-lft-identity
6×add-exp-log sqrt-prod add-cbrt-cube
4×sqrt-div add-log-exp
3×associate-*r* associate-*l*
2×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+
1×sin-sum pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
4 → 56
Calls
4 calls:
3.0ms
(* (atan2 x.im x.re) y.re)
4.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
3.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
6.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

series242.0ms

Counts
4 → 12
Calls
4 calls:
16.0ms
(* (atan2 x.im x.re) y.re)
39.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
37.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))
150.0ms
(sin (+ (* (log (sqrt (+ (* x.re x.re) (* x.im x.im)))) y.im) (* (atan2 x.im x.re) y.re)))

simplify75.0ms

Algorithm
egg-herbie
Counts
68 → 68
Iterations

Useful iterations: 2 (14.0ms)

IterNodesCost
0194425
1496388
21117386
32390386
45002386

prune314.0ms

Filtered
68 candidates to 54 candidates (79.4%)
Pruning

11 alts after pruning (9 fresh and 2 done)

PrunedKeptTotal
New68068
Fresh099
Picked011
Done011
Total681179

Merged error: 18.4b

Counts
79 → 11

localize24.0ms

Local error

Found 4 expressions with local error:

1.3b
(* (atan2 x.im x.re) y.im)
1.3b
(* (atan2 x.im x.re) y.re)
18.4b
(sin (- (* (atan2 x.im x.re) y.re) (* y.im (log (/ -1 x.re)))))
29.3b
(sqrt (+ (* x.re x.re) (* x.im x.im)))

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
9×pow1 add-cube-cbrt *-un-lft-identity
8×add-exp-log add-cbrt-cube
6×associate-*r* associate-*l*
4×add-log-exp
3×sqrt-prod
2×sin-sum sqrt-div pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 sin-diff flip-+
Counts
4 → 61
Calls
4 calls:
3.0ms
(* (atan2 x.im x.re) y.im)
4.0ms
(* (atan2 x.im x.re) y.re)
4.0ms
(sin (- (* (atan2 x.im x.re) y.re) (* y.im (log (/ -1 x.re)))))
4.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

series193.0ms

Counts
4 → 12
Calls
4 calls:
16.0ms
(* (atan2 x.im x.re) y.im)
17.0ms
(* (atan2 x.im x.re) y.re)
118.0ms
(sin (- (* (atan2 x.im x.re) y.re) (* y.im (log (/ -1 x.re)))))
42.0ms
(sqrt (+ (* x.re x.re) (* x.im x.im)))

simplify88.0ms

Algorithm
egg-herbie
Counts
73 → 73
Iterations

Useful iterations: 2 (18.0ms)

IterNodesCost
0254403
1691362
21619359
33213359
45002359

prune274.0ms

Filtered
73 candidates to 51 candidates (69.9%)
Pruning

13 alts after pruning (10 fresh and 3 done)

PrunedKeptTotal
New71273
Fresh088
Picked011
Done022
Total711384

Merged error: 12.3b

Counts
84 → 13

regimes466.0ms

bsearch6.0ms

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