Details

Time bar (total: 9.6s)

analyze149.0ms (1.6%)

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
25%74.9%0.1%5
25%62.4%12.6%6
31.2%50%18.8%7
40.6%37.5%22%8
45.3%26.5%28.2%9
46.8%19.5%33.7%10
48.8%14%37.2%11
51.7%10.1%38.1%12
52.8%7.1%40.1%13
53.3%5.1%41.6%14
Compiler

Compiled 20 to 12 computations (40% saved)

sample25.0ms (0.3%)

Algorithm
intervals
Results
15.0ms256×body128valid
1.0ms14×body128invalid
Compiler

Compiled 39 to 25 computations (35.9% saved)

simplify325.0ms (3.4%)

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (201.0ms)

IterNodesCost
0495620
1495620

prune8.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Error
8.8b
Counts
2 → 2
Compiler

Compiled 41 to 29 computations (29.3% saved)

localize11.0ms (0.1%)

Local error

Found 8 expressions with local error:

8.3b
(*.f64 (-.f64 (*.f64 x.re x.re) (*.f64 x.im x.im)) x.re)
0.1b
(*.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)) x.im)
0.1b
(-.f64 (*.f64 (-.f64 (*.f64 x.re x.re) (*.f64 x.im x.im)) x.re) (*.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)) x.im))
0.0b
(+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re))
0.0b
(+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re))
0.1b
(-.f64 (*.f64 (-.f64 (*.f64 x.re x.re) (*.f64 x.im x.im)) x.re) (*.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)) x.im))
0.1b
(*.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)) x.im)
8.3b
(*.f64 (-.f64 (*.f64 x.re x.re) (*.f64 x.im x.im)) x.re)

rewrite43.0ms (0.5%)

Algorithm
rewrite-expression-head
Rules
12×associate-*l/_binary64_3090 add-sqr-sqrt_binary64_3169
*-un-lft-identity_binary64_3147 add-exp-log_binary64_3185 add-cbrt-cube_binary64_3183 pow1_binary64_3208 add-log-exp_binary64_3186 add-cube-cbrt_binary64_3182
associate-*l*_binary64_3088
associate-*r*_binary64_3087
flip--_binary64_3122 flip-+_binary64_3121 flip3--_binary64_3151 flip3-+_binary64_3150 frac-sub_binary64_3156
*-commutative_binary64_3078 unswap-sqr_binary64_3115 pow-prod-down_binary64_3218 prod-exp_binary64_3196 cbrt-unprod_binary64_3180
cancel-sign-sub-inv_binary64_3113 sub-neg_binary64_3140 +-commutative_binary64_3077 difference-of-squares_binary64_3116 diff-log_binary64_3239 sum-log_binary64_3238
Counts
4 → 68
Calls

8 calls:

15.0ms
(-.f64 (*.f64 (-.f64 (*.f64 x.re x.re) (*.f64 x.im x.im)) x.re) (*.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)) x.im))
10.0ms
(*.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)) x.im)
7.0ms
(*.f64 (-.f64 (*.f64 x.re x.re) (*.f64 x.im x.im)) x.re)
4.0ms
(+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re))
0.0ms
(+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re))

series689.0ms (7.2%)

Counts
4 → 36
Calls

4 calls:

261.0ms
(-.f64 (*.f64 (-.f64 (*.f64 x.re x.re) (*.f64 x.im x.im)) x.re) (*.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)) x.im))
208.0ms
(*.f64 (-.f64 (*.f64 x.re x.re) (*.f64 x.im x.im)) x.re)
114.0ms
(*.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)) x.im)
105.0ms
(+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re))
Compiler

Compiled 888 to 648 computations (27% saved)

simplify70.0ms (0.7%)

Algorithm
egg-herbie
Counts
104 → 104
Iterations

Useful iterations: 0 (26.0ms)

IterNodesCost
046912004
146912004

prune217.0ms (2.3%)

Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New995104
Fresh011
Picked101
Done000
Total1006106
Error
0.0b
Counts
106 → 6
Compiler

Compiled 2369 to 997 computations (57.9% saved)

localize12.0ms (0.1%)

Local error

Found 8 expressions with local error:

0.1b
(*.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)) x.im)
0.1b
(-.f64 (*.f64 (+.f64 x.re x.im) (*.f64 x.re (-.f64 x.re x.im))) (*.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)) x.im))
0.0b
(*.f64 x.re (-.f64 x.re x.im))
0.0b
(+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re))
0.0b
(*.f64 x.re (-.f64 x.re x.im))
0.1b
(-.f64 (*.f64 (+.f64 x.re x.im) (*.f64 x.re (-.f64 x.re x.im))) (*.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)) x.im))
0.1b
(*.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)) x.im)
0.1b
(*.f64 (+.f64 x.re x.im) (*.f64 x.re (-.f64 x.re x.im)))

rewrite98.0ms (1%)

Algorithm
rewrite-expression-head
Rules
36×distribute-lft-in_binary64_3096 distribute-rgt-in_binary64_3097
31×cancel-sign-sub-inv_binary64_3113
26×associate-*r/_binary64_3089
25×add-sqr-sqrt_binary64_3169
24×associate-*l/_binary64_3090
23×*-un-lft-identity_binary64_3147
19×add-cube-cbrt_binary64_3182
18×flip-+_binary64_3121 flip3-+_binary64_3150
16×associate--l+_binary64_3084 frac-sub_binary64_3156
13×add-exp-log_binary64_3185 add-cbrt-cube_binary64_3183 pow1_binary64_3208
12×frac-times_binary64_3157
11×flip--_binary64_3122 flip3--_binary64_3151 sub-neg_binary64_3140
10×associate-*l*_binary64_3088
associate-*r*_binary64_3087
add-log-exp_binary64_3186
pow-prod-down_binary64_3218 prod-exp_binary64_3196 cbrt-unprod_binary64_3180
*-commutative_binary64_3078
unswap-sqr_binary64_3115
distribute-lft-out_binary64_3098 distribute-lft-out--_binary64_3099 difference-of-squares_binary64_3116 diff-log_binary64_3239
Counts
4 → 137
Calls

8 calls:

28.0ms
(-.f64 (*.f64 (+.f64 x.re x.im) (*.f64 x.re (-.f64 x.re x.im))) (*.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)) x.im))
14.0ms
(*.f64 x.re (-.f64 x.re x.im))
13.0ms
(*.f64 (+.f64 x.re x.im) (*.f64 x.re (-.f64 x.re x.im)))
9.0ms
(*.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)) x.im)
0.0ms
(+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re))

series679.0ms (7.1%)

Counts
4 → 42
Calls

4 calls:

246.0ms
(-.f64 (*.f64 (+.f64 x.re x.im) (*.f64 x.re (-.f64 x.re x.im))) (*.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)) x.im))
241.0ms
(*.f64 (+.f64 x.re x.im) (*.f64 x.re (-.f64 x.re x.im)))
113.0ms
(*.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)) x.im)
78.0ms
(*.f64 x.re (-.f64 x.re x.im))
Compiler

Compiled 1044 to 726 computations (30.5% saved)

simplify157.0ms (1.6%)

Algorithm
egg-herbie
Counts
179 → 179
Iterations

Useful iterations: 0 (80.0ms)

IterNodesCost
047164129
147164129

prune259.0ms (2.7%)

Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New1754179
Fresh235
Picked101
Done000
Total1787185
Error
0.0b
Counts
185 → 7
Compiler

Compiled 4325 to 1506 computations (65.2% saved)

localize22.0ms (0.2%)

Local error

Found 8 expressions with local error:

0.1b
(+.f64 (*.f64 x.re (+.f64 x.re x.im)) (*.f64 2 (*.f64 x.re x.im)))
0.0b
(*.f64 x.re (+.f64 x.re x.im))
0.0b
(+.f64 (*.f64 (*.f64 x.re x.re) (+.f64 x.re x.im)) (*.f64 (neg.f64 x.im) (+.f64 (*.f64 x.re (+.f64 x.re x.im)) (*.f64 2 (*.f64 x.re x.im)))))
0.0b
(*.f64 2 (*.f64 x.re x.im))
0.0b
(*.f64 x.re (+.f64 x.re x.im))
0.1b
(+.f64 (*.f64 x.re (+.f64 x.re x.im)) (*.f64 2 (*.f64 x.re x.im)))
0.2b
(*.f64 (neg.f64 x.im) (+.f64 (*.f64 x.re (+.f64 x.re x.im)) (*.f64 2 (*.f64 x.re x.im))))
6.7b
(*.f64 (*.f64 x.re x.re) (+.f64 x.re x.im))

rewrite50.0ms (0.5%)

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt_binary64_3169
15×*-un-lft-identity_binary64_3147
14×associate-*l*_binary64_3088
13×add-exp-log_binary64_3185 add-cbrt-cube_binary64_3183 pow1_binary64_3208
11×associate-*r*_binary64_3087 add-cube-cbrt_binary64_3182
add-log-exp_binary64_3186 associate-*r/_binary64_3089
pow-prod-down_binary64_3218 prod-exp_binary64_3196 cbrt-unprod_binary64_3180
flip-+_binary64_3121 flip3-+_binary64_3150 distribute-lft-in_binary64_3096 distribute-rgt-in_binary64_3097
*-commutative_binary64_3078 unswap-sqr_binary64_3115 distribute-lft-neg-in_binary64_3104 distribute-rgt-neg-in_binary64_3105
associate-+l+_binary64_3080 distribute-lft-out_binary64_3098
neg-mul-1_binary64_3143 +-commutative_binary64_3077 distribute-lft-neg-out_binary64_3106 sum-log_binary64_3238
Counts
4 → 90
Calls

8 calls:

15.0ms
(+.f64 (*.f64 x.re (+.f64 x.re x.im)) (*.f64 2 (*.f64 x.re x.im)))
11.0ms
(*.f64 (neg.f64 x.im) (+.f64 (*.f64 x.re (+.f64 x.re x.im)) (*.f64 2 (*.f64 x.re x.im))))
8.0ms
(*.f64 (*.f64 x.re x.re) (+.f64 x.re x.im))
8.0ms
(*.f64 x.re (+.f64 x.re x.im))
0.0ms
(*.f64 2 (*.f64 x.re x.im))

series602.0ms (6.3%)

Counts
4 → 48
Calls

4 calls:

226.0ms
(*.f64 (neg.f64 x.im) (+.f64 (*.f64 x.re (+.f64 x.re x.im)) (*.f64 2 (*.f64 x.re x.im))))
135.0ms
(+.f64 (*.f64 x.re (+.f64 x.re x.im)) (*.f64 2 (*.f64 x.re x.im)))
121.0ms
(*.f64 (*.f64 x.re x.re) (+.f64 x.re x.im))
120.0ms
(*.f64 x.re (+.f64 x.re x.im))
Compiler

Compiled 1494 to 1047 computations (29.9% saved)

simplify103.0ms (1.1%)

Algorithm
egg-herbie
Counts
138 → 138
Iterations

Useful iterations: 0 (69.0ms)

IterNodesCost
051642113

prune208.0ms (2.2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New1371138
Fresh156
Picked011
Done000
Total1387145
Error
0b
Counts
145 → 7
Compiler

Compiled 3382 to 1225 computations (63.8% saved)

localize23.0ms (0.2%)

Local error

Found 8 expressions with local error:

0.2b
(*.f64 x.im (*.f64 x.re (+.f64 x.re (*.f64 x.im 3))))
0.1b
(*.f64 x.re (+.f64 x.re (*.f64 x.im 3)))
0.0b
(+.f64 x.re (*.f64 x.im 3))
0.0b
(+.f64 (*.f64 (*.f64 x.re x.re) (+.f64 x.re x.im)) (neg.f64 (*.f64 x.im (*.f64 x.re (+.f64 x.re (*.f64 x.im 3))))))
0.0b
(+.f64 x.re (*.f64 x.im 3))
0.1b
(*.f64 x.re (+.f64 x.re (*.f64 x.im 3)))
0.2b
(*.f64 x.im (*.f64 x.re (+.f64 x.re (*.f64 x.im 3))))
6.7b
(*.f64 (*.f64 x.re x.re) (+.f64 x.re x.im))

rewrite57.0ms (0.6%)

Algorithm
rewrite-expression-head
Rules
16×add-exp-log_binary64_3185 add-cbrt-cube_binary64_3183 pow1_binary64_3208
11×add-sqr-sqrt_binary64_3169
10×*-un-lft-identity_binary64_3147
associate-*r*_binary64_3087 add-cube-cbrt_binary64_3182 associate-*r/_binary64_3089
pow-prod-down_binary64_3218 prod-exp_binary64_3196 cbrt-unprod_binary64_3180 associate-*l*_binary64_3088
distribute-lft-in_binary64_3096 add-log-exp_binary64_3186 distribute-rgt-in_binary64_3097
flip-+_binary64_3121 flip3-+_binary64_3150
*-commutative_binary64_3078
unswap-sqr_binary64_3115
distribute-lft-out_binary64_3098 +-commutative_binary64_3077 sum-log_binary64_3238
Counts
4 → 81
Calls

8 calls:

15.0ms
(*.f64 (*.f64 x.re x.re) (+.f64 x.re x.im))
13.0ms
(*.f64 x.im (*.f64 x.re (+.f64 x.re (*.f64 x.im 3))))
10.0ms
(*.f64 x.re (+.f64 x.re (*.f64 x.im 3)))
5.0ms
(+.f64 x.re (*.f64 x.im 3))
0.0ms
(+.f64 (*.f64 (*.f64 x.re x.re) (+.f64 x.re x.im)) (neg.f64 (*.f64 x.im (*.f64 x.re (+.f64 x.re (*.f64 x.im 3))))))

series517.0ms (5.4%)

Counts
4 → 48
Calls

4 calls:

199.0ms
(*.f64 x.im (*.f64 x.re (+.f64 x.re (*.f64 x.im 3))))
116.0ms
(*.f64 (*.f64 x.re x.re) (+.f64 x.re x.im))
107.0ms
(+.f64 x.re (*.f64 x.im 3))
95.0ms
(*.f64 x.re (+.f64 x.re (*.f64 x.im 3)))
Compiler

Compiled 1320 to 939 computations (28.9% saved)

simplify147.0ms (1.5%)

Algorithm
egg-herbie
Counts
129 → 129
Iterations

Useful iterations: 0 (102.0ms)

IterNodesCost
049601818
149601818

prune134.0ms (1.4%)

Pruning

7 alts after pruning (5 fresh and 2 done)

PrunedKeptTotal
New1290129
Fresh055
Picked011
Done011
Total1297136
Error
0b
Counts
136 → 7
Compiler

Compiled 2671 to 1278 computations (52.2% saved)

simplify191.0ms (2%)

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (157.0ms)

IterNodesCost
034031952
134031952

regimes268.0ms (2.8%)

Accuracy

Total 0.2b remaining (99%)

Threshold costs 0.2b (99%)

Compiler

Compiled 1988 to 1172 computations (41% saved)

bsearch0.0ms (0%)

simplify5.0ms (0.1%)

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
06438
16438

end0.0ms (0%)

sample4.5s (47%)

Algorithm
intervals
Results
543.0ms8000×body128valid
26.0ms384×body128invalid
Compiler

Compiled 3013 to 1771 computations (41.2% saved)

Pareto

0.39712465563007215

Profiling

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