Details

Time bar (total: 11.3s)

analyze519.0ms (4.6%)

Algorithm
search
Search
TrueOtherFalseIter
0%99.8%0.2%0
0%99.8%0.2%1
0%99.8%0.2%2
0%99.8%0.2%3
0%99.8%0.2%4
0%99.8%0.2%5
0%99.8%0.2%6
0%99.8%0.2%7
6.2%93.6%0.2%8
25%74.9%0.2%9
28.1%71.7%0.2%10
29.6%70.2%0.2%11
53%46.8%0.2%12
71.3%28.5%0.2%13
71.7%28.1%0.2%14
Compiler

Compiled 16 to 12 computations (25% saved)

sample21.0ms (0.2%)

Algorithm
intervals
Results
10.0ms256×body128valid
1.0ms14×body128invalid
Compiler

Compiled 31 to 27 computations (12.9% saved)

simplify217.0ms (1.9%)

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (125.0ms)

IterNodesCost
0523230

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Error
27.3b
Counts
2 → 1
Compiler

Compiled 30 to 22 computations (26.7% saved)

localize10.0ms (0.1%)

Local error

Found 6 expressions with local error:

26.8b
(/.f64 (-.f64 (*.f64 x.im y.re) (*.f64 x.re y.im)) (+.f64 (*.f64 y.re y.re) (*.f64 y.im y.im)))
0.2b
(-.f64 (*.f64 x.im y.re) (*.f64 x.re y.im))
0.0b
(+.f64 (*.f64 y.re y.re) (*.f64 y.im y.im))
0.0b
(+.f64 (*.f64 y.re y.re) (*.f64 y.im y.im))
0.2b
(-.f64 (*.f64 x.im y.re) (*.f64 x.re y.im))
26.8b
(/.f64 (-.f64 (*.f64 x.im y.re) (*.f64 x.re y.im)) (+.f64 (*.f64 y.re y.re) (*.f64 y.im y.im)))

rewrite22.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt_binary64_1123 *-un-lft-identity_binary64_1101 add-cube-cbrt_binary64_1136
times-frac_binary64_1107
add-log-exp_binary64_1140
add-exp-log_binary64_1139 add-cbrt-cube_binary64_1137
pow1_binary64_1162 associate-/l*_binary64_1046 associate-/r*_binary64_1045
flip--_binary64_1076 flip3--_binary64_1105 flip3-+_binary64_1104 associate-/l/_binary64_1048 associate-/r/_binary64_1047 flip-+_binary64_1075
diff-log_binary64_1193 frac-2neg_binary64_1112 sum-log_binary64_1192 sub-neg_binary64_1094 clear-num_binary64_1100 div-inv_binary64_1098 +-commutative_binary64_1031 div-exp_binary64_1152 cbrt-undiv_binary64_1135 cancel-sign-sub-inv_binary64_1067 div-sub_binary64_1106
Counts
3 → 55
Calls

6 calls:

9.0ms
(/.f64 (-.f64 (*.f64 x.im y.re) (*.f64 x.re y.im)) (+.f64 (*.f64 y.re y.re) (*.f64 y.im y.im)))
4.0ms
(+.f64 (*.f64 y.re y.re) (*.f64 y.im y.im))
4.0ms
(-.f64 (*.f64 x.im y.re) (*.f64 x.re y.im))
0.0ms
(+.f64 (*.f64 y.re y.re) (*.f64 y.im y.im))
0.0ms
(-.f64 (*.f64 x.im y.re) (*.f64 x.re y.im))

series580.0ms (5.1%)

Counts
3 → 63
Calls

3 calls:

338.0ms
(/.f64 (-.f64 (*.f64 x.im y.re) (*.f64 x.re y.im)) (+.f64 (*.f64 y.re y.re) (*.f64 y.im y.im)))
152.0ms
(-.f64 (*.f64 x.im y.re) (*.f64 x.re y.im))
90.0ms
(+.f64 (*.f64 y.re y.re) (*.f64 y.im y.im))
Compiler

Compiled 1407 to 1170 computations (16.8% saved)

simplify94.0ms (0.8%)

Algorithm
egg-herbie
Counts
118 → 118
Iterations

Useful iterations: 0 (62.0ms)

IterNodesCost
060892687

prune188.0ms (1.7%)

Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New10810118
Fresh000
Picked101
Done000
Total10910119
Error
4.2b
Counts
119 → 10
Compiler

Compiled 2391 to 868 computations (63.7% saved)

localize17.0ms (0.1%)

Local error

Found 8 expressions with local error:

0.2b
(-.f64 (*.f64 x.im y.re) (*.f64 x.re y.im))
0.1b
(/.f64 (/.f64 (-.f64 (*.f64 x.im y.re) (*.f64 x.re y.im)) (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))) (sqrt.f64 (+.f64 (*.f64 y.re y.re) (*.f64 y.im y.im))))
0.0b
(+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))
0.0b
(+.f64 (*.f64 y.re y.re) (*.f64 y.im y.im))
0.2b
(-.f64 (*.f64 x.im y.re) (*.f64 x.re y.im))
17.8b
(/.f64 (-.f64 (*.f64 x.im y.re) (*.f64 x.re y.im)) (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))
27.8b
(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
27.8b
(sqrt.f64 (+.f64 (*.f64 y.re y.re) (*.f64 y.im y.im)))

rewrite40.0ms (0.4%)

Algorithm
rewrite-expression-head
Rules
43×*-un-lft-identity_binary64_1101
28×sqrt-prod_binary64_1117
25×add-sqr-sqrt_binary64_1123
24×times-frac_binary64_1107
23×add-cube-cbrt_binary64_1136
10×unpow-prod-down_binary64_1180 distribute-lft-out_binary64_1052
associate-/r*_binary64_1045
add-log-exp_binary64_1140 add-exp-log_binary64_1139 pow1_binary64_1162 add-cbrt-cube_binary64_1137 sqrt-div_binary64_1118
flip3-+_binary64_1104 associate-/l*_binary64_1046 flip-+_binary64_1075
rem-sqrt-square_binary64_1114 sqrt-pow1_binary64_1119 flip--_binary64_1076 flip3--_binary64_1105 associate-/l/_binary64_1048 associate-/r/_binary64_1047 pow1/2_binary64_1181
diff-log_binary64_1193 frac-2neg_binary64_1112 sub-neg_binary64_1094 clear-num_binary64_1100 div-inv_binary64_1098 div-exp_binary64_1152 cbrt-undiv_binary64_1135 cancel-sign-sub-inv_binary64_1067 div-sub_binary64_1106
Counts
4 → 96
Calls

8 calls:

14.0ms
(/.f64 (-.f64 (*.f64 x.im y.re) (*.f64 x.re y.im)) (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))
8.0ms
(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
4.0ms
(sqrt.f64 (+.f64 (*.f64 y.re y.re) (*.f64 y.im y.im)))
4.0ms
(-.f64 (*.f64 x.im y.re) (*.f64 x.re y.im))
0.0ms
(+.f64 (*.f64 y.re y.re) (*.f64 y.im y.im))

series835.0ms (7.4%)

Counts
4 → 94
Calls

4 calls:

437.0ms
(/.f64 (-.f64 (*.f64 x.im y.re) (*.f64 x.re y.im)) (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))
158.0ms
(-.f64 (*.f64 x.im y.re) (*.f64 x.re y.im))
123.0ms
(sqrt.f64 (+.f64 (*.f64 y.re y.re) (*.f64 y.im y.im)))
116.0ms
(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
Compiler

Compiled 3466 to 2706 computations (21.9% saved)

simplify98.0ms (0.9%)

Algorithm
egg-herbie
Counts
190 → 190
Iterations

Useful iterations: 0 (47.0ms)

IterNodesCost
051614969

prune264.0ms (2.3%)

Pruning

13 alts after pruning (12 fresh and 1 done)

PrunedKeptTotal
New1864190
Fresh189
Picked011
Done000
Total18713200
Error
4.2b
Counts
200 → 13
Compiler

Compiled 5907 to 2427 computations (58.9% saved)

localize14.0ms (0.1%)

Local error

Found 8 expressions with local error:

0.3b
(*.f64 (/.f64 1 (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))) (/.f64 (-.f64 (*.f64 x.im y.re) (*.f64 x.re y.im)) (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))))
0.2b
(-.f64 (*.f64 x.im y.re) (*.f64 x.re y.im))
0.0b
(+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))
0.0b
(+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))
0.3b
(*.f64 (/.f64 1 (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))) (/.f64 (-.f64 (*.f64 x.im y.re) (*.f64 x.re y.im)) (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))))
17.8b
(/.f64 (-.f64 (*.f64 x.im y.re) (*.f64 x.re y.im)) (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))
27.8b
(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
27.8b
(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))

rewrite101.0ms (0.9%)

Algorithm
rewrite-expression-head
Rules
107×*-un-lft-identity_binary64_1101
101×add-sqr-sqrt_binary64_1123
94×times-frac_binary64_1107
71×sqrt-prod_binary64_1117
53×add-cube-cbrt_binary64_1136
30×associate-*r*_binary64_1041 associate-*l*_binary64_1042
28×add-exp-log_binary64_1139
24×unpow-prod-down_binary64_1180 distribute-lft-out_binary64_1052
18×add-cbrt-cube_binary64_1137
15×unswap-sqr_binary64_1069
10×sqrt-div_binary64_1118
div-exp_binary64_1152
prod-exp_binary64_1150 pow1_binary64_1162 associate-/r*_binary64_1045
associate-/r/_binary64_1047
flip3-+_binary64_1104 cbrt-undiv_binary64_1135 flip-+_binary64_1075
cbrt-unprod_binary64_1134 add-log-exp_binary64_1140
div-inv_binary64_1098 associate-/l*_binary64_1046
1-exp_binary64_1145 rem-sqrt-square_binary64_1114 sqrt-pow1_binary64_1119 associate-/l/_binary64_1048 rec-exp_binary64_1151 pow1/2_binary64_1181
*-commutative_binary64_1032 frac-times_binary64_1111 frac-2neg_binary64_1112 clear-num_binary64_1100 flip--_binary64_1076 flip3--_binary64_1105 associate-*r/_binary64_1043 pow-prod-down_binary64_1172 associate-*l/_binary64_1044 div-sub_binary64_1106
Counts
4 → 185
Calls

8 calls:

45.0ms
(*.f64 (/.f64 1 (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))) (/.f64 (-.f64 (*.f64 x.im y.re) (*.f64 x.re y.im)) (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))))
14.0ms
(/.f64 (-.f64 (*.f64 x.im y.re) (*.f64 x.re y.im)) (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))
8.0ms
(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
8.0ms
(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
0.0ms
(+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))

series1.0s (9.1%)

Counts
4 → 97
Calls

4 calls:

442.0ms
(/.f64 (-.f64 (*.f64 x.im y.re) (*.f64 x.re y.im)) (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))
337.0ms
(*.f64 (/.f64 1 (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))) (/.f64 (-.f64 (*.f64 x.im y.re) (*.f64 x.re y.im)) (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))))
123.0ms
(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
123.0ms
(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
Compiler

Compiled 3435 to 2910 computations (15.3% saved)

simplify151.0ms (1.3%)

Algorithm
egg-herbie
Counts
282 → 282
Iterations

Useful iterations: 0 (53.0ms)

IterNodesCost
049939980
149939980

prune536.0ms (4.8%)

Pruning

12 alts after pruning (10 fresh and 2 done)

PrunedKeptTotal
New2802282
Fresh3811
Picked011
Done011
Total28312295
Error
4.0b
Counts
295 → 12
Compiler

Compiled 9298 to 5463 computations (41.2% saved)

localize23.0ms (0.2%)

Local error

Found 8 expressions with local error:

0.1b
(/.f64 (/.f64 (-.f64 (*.f64 x.im y.re) (*.f64 x.re y.im)) (*.f64 (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))))) (sqrt.f64 (+.f64 (*.f64 y.re y.re) (*.f64 y.im y.im))))
0.0b
(+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))
0.0b
(+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))
0.0b
(+.f64 (*.f64 y.re y.re) (*.f64 y.im y.im))
17.8b
(/.f64 (-.f64 (*.f64 x.im y.re) (*.f64 x.re y.im)) (*.f64 (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))))
27.8b
(sqrt.f64 (+.f64 (*.f64 y.re y.re) (*.f64 y.im y.im)))
27.8b
(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
27.8b
(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))

rewrite61.0ms (0.5%)

Algorithm
rewrite-expression-head
Rules
30×sqrt-div_binary64_1118
17×*-un-lft-identity_binary64_1101
13×sqrt-prod_binary64_1117
12×add-sqr-sqrt_binary64_1123
add-exp-log_binary64_1139 flip3-+_binary64_1104 add-cube-cbrt_binary64_1136 add-cbrt-cube_binary64_1137 flip-+_binary64_1075
associate-/r/_binary64_1047
pow1_binary64_1162
unpow-prod-down_binary64_1180 frac-times_binary64_1111 add-log-exp_binary64_1140 distribute-lft-out_binary64_1052
rem-sqrt-square_binary64_1114 sqrt-pow1_binary64_1119 associate-/l*_binary64_1046 times-frac_binary64_1107 pow1/2_binary64_1181
associate-/l/_binary64_1048 associate-*r/_binary64_1043 div-exp_binary64_1152 cbrt-undiv_binary64_1135 associate-*l/_binary64_1044
cbrt-unprod_binary64_1134 prod-exp_binary64_1150 frac-2neg_binary64_1112 clear-num_binary64_1100 flip--_binary64_1076 flip3--_binary64_1105 div-inv_binary64_1098 associate-/r*_binary64_1045 div-sub_binary64_1106
Counts
4 → 81
Calls

8 calls:

29.0ms
(/.f64 (-.f64 (*.f64 x.im y.re) (*.f64 x.re y.im)) (*.f64 (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))))
9.0ms
(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
8.0ms
(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
4.0ms
(sqrt.f64 (+.f64 (*.f64 y.re y.re) (*.f64 y.im y.im)))
0.0ms
(+.f64 (*.f64 y.re y.re) (*.f64 y.im y.im))

series854.0ms (7.6%)

Counts
4 → 89
Calls

4 calls:

447.0ms
(/.f64 (-.f64 (*.f64 x.im y.re) (*.f64 x.re y.im)) (*.f64 (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))))
142.0ms
(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
134.0ms
(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
131.0ms
(sqrt.f64 (+.f64 (*.f64 y.re y.re) (*.f64 y.im y.im)))
Compiler

Compiled 4191 to 3278 computations (21.8% saved)

simplify87.0ms (0.8%)

Algorithm
egg-herbie
Counts
170 → 170
Iterations

Useful iterations: 0 (45.0ms)

IterNodesCost
051964055

prune285.0ms (2.5%)

Pruning

12 alts after pruning (9 fresh and 3 done)

PrunedKeptTotal
New1700170
Fresh099
Picked011
Done022
Total17012182
Error
4.0b
Counts
182 → 12
Compiler

Compiled 6243 to 3106 computations (50.2% saved)

simplify34.0ms (0.3%)

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (6.0ms)

IterNodesCost
04232333
14232333

regimes1.1s (9.7%)

Compiler

Compiled 6226 to 4607 computations (26% saved)

bsearch89.0ms (0.8%)

Steps
ItersRangePoint
7
3.8868018845307633e+68
1.3644531650600456e+70
2.0139063475555305e+69
9
1.5985712979139024e-152
5.795803614072852e-145
1.8192329406445362e-149
9
-7.750398627192034e-42
-7.035472584919937e-50
-8.232708701844971e-48
7
-5.3171984657535355e+81
-5.6545501491607255e+79
-3.2563987087522574e+81
Compiler

Compiled 1 to 4 computations (-300% saved)

regimes719.0ms (6.4%)

Compiler

Compiled 3081 to 2412 computations (21.7% saved)

bsearch75.0ms (0.7%)

Steps
ItersRangePoint
7
3.8868018845307633e+68
1.3644531650600456e+70
1.2069815748150215e+69
9
1.5985712979139024e-152
5.795803614072852e-145
1.3404554011445771e-145
9
-7.750398627192034e-42
-7.035472584919937e-50
-1.2878803517827424e-49
7
-5.3171984657535355e+81
-5.6545501491607255e+79
-2.3901732992931246e+81
Compiler

Compiled 1 to 4 computations (-300% saved)

regimes265.0ms (2.4%)

Compiler

Compiled 431 to 477 computations (-10.7% saved)

bsearch76.0ms (0.7%)

Steps
ItersRangePoint
7
3.8868018845307633e+68
1.3644531650600456e+70
1.2946963342904071e+70
9
1.5985712979139024e-152
5.795803614072852e-145
3.8908836956847665e-149
9
-7.750398627192034e-42
-7.035472584919937e-50
-7.146998424621189e-50
7
-5.3171984657535355e+81
-5.6545501491607255e+79
-5.2209511980358546e+81
Compiler

Compiled 1 to 4 computations (-300% saved)

regimes228.0ms (2%)

Compiler

Compiled 376 to 427 computations (-13.6% saved)

bsearch76.0ms (0.7%)

Steps
ItersRangePoint
7
3.8868018845307633e+68
1.3644531650600456e+70
1.3505017989061179e+70
9
1.5985712979139024e-152
5.795803614072852e-145
9.118125018073582e-148
8
-4.645076202524181e-240
-1.264600105933541e-242
-4.6048343682484033e-240
7
-5.3171984657535355e+81
-5.6545501491607255e+79
-5.2209511980358546e+81
Compiler

Compiled 1 to 4 computations (-300% saved)

regimes160.0ms (1.4%)

Compiler

Compiled 140 to 212 computations (-51.4% saved)

bsearch78.0ms (0.7%)

Steps
ItersRangePoint
9
2.9440458580396446e+54
2.424121438622175e+63
9.247055853391496e+58
10
6.981770734925066e+31
3.110364680802558e+44
3.4647570315662663e+40
10
1.6166047791524876e-70
1.2799929126807054e-59
2.954263000042488e-61
8
-1.830820577979186e-12
-5.592649249220658e-17
-5.812131874856144e-13
Compiler

Compiled 1 to 4 computations (-300% saved)

regimes102.0ms (0.9%)

Compiler

Compiled 48 to 136 computations (-183.3% saved)

bsearch30.0ms (0.3%)

Steps
ItersRangePoint
7
4.980887860223029e-07
0.00010323440451509003
5.872366693829185e-06
8
-3.702281864159641e+74
-6.13376548996517e+71
-8.128458494529882e+71
Compiler

Compiled 1 to 4 computations (-300% saved)

regimes62.0ms (0.5%)

Compiler

Compiled 32 to 112 computations (-250% saved)

bsearch28.0ms (0.2%)

Steps
ItersRangePoint
8
2.443870323434491e+43
1.5554586086373416e+46
1.5347938031871036e+46
7
-1.466580252871722e+116
-5.105510058682821e+114
-6.4465228986931395e+115
Compiler

Compiled 1 to 4 computations (-300% saved)

regimes33.0ms (0.3%)

Accuracy

Total 10.4b remaining (68.7%)

Threshold costs 0b (0%)

Compiler

Compiled 20 to 92 computations (-360% saved)

bsearch14.0ms (0.1%)

Compiler

Compiled 375 to 213 computations (43.2% saved)

simplify10.0ms (0.1%)

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (3.0ms)

IterNodesCost
0157705
1157705

end0.0ms (0%)

sample2.1s (18.3%)

Algorithm
intervals
Results
327.0ms8000×body128valid
25.0ms477×body128invalid
Compiler

Compiled 1616 to 1131 computations (30% saved)

Pareto

0.940683111466712

Profiling

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