Details

Time bar (total: 15.0s)

analyze1.2s (8.2%)

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
9.4%90.4%0.2%6
17.2%82.7%0.2%7
19.5%80.3%0.2%8
30.8%69%0.2%9
35.5%64.3%0.2%10
42.4%57.4%0.2%11
47.1%52.7%0.2%12
49%50.8%0.2%13
50.1%49.7%0.2%14
Compiler

Compiled 38 to 20 computations (47.4% saved)

sample132.0ms (0.9%)

Algorithm
intervals
Results
52.0ms89×body1024invalid
27.0ms238×body128valid
10.0ms29×body512invalid
4.0msbody2048invalid
4.0ms14×body256invalid
3.0msbody1024valid
2.0ms19×body128invalid
2.0msbody512valid
2.0msbody256valid
Compiler

Compiled 75 to 43 computations (42.7% saved)

simplify168.0ms (1.1%)

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (66.0ms)

IterNodesCost
0494472
1494472

prune13.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New101
Fresh011
Picked000
Done000
Total112
Error
36.1b
Counts
2 → 1
Compiler

Compiled 73 to 38 computations (47.9% saved)

localize24.0ms (0.2%)

Local error

Found 8 expressions with local error:

0.0b
(-.f64 (*.f64 (log.f64 (sqrt.f64 (+.f64 (*.f64 x.re x.re) (*.f64 x.im x.im)))) y.re) (*.f64 (atan2.f64 x.im x.re) y.im))
0.0b
(*.f64 (exp.f64 (-.f64 (*.f64 (log.f64 (sqrt.f64 (+.f64 (*.f64 x.re x.re) (*.f64 x.im x.im)))) y.re) (*.f64 (atan2.f64 x.im x.re) y.im))) (sin.f64 (+.f64 (*.f64 (log.f64 (sqrt.f64 (+.f64 (*.f64 x.re x.re) (*.f64 x.im x.im)))) y.im) (*.f64 (atan2.f64 x.im x.re) y.re))))
0.0b
(+.f64 (*.f64 x.re x.re) (*.f64 x.im x.im))
0.0b
(+.f64 (*.f64 x.re x.re) (*.f64 x.im x.im))
1.5b
(*.f64 (atan2.f64 x.im x.re) y.im)
29.8b
(sin.f64 (+.f64 (*.f64 (log.f64 (sqrt.f64 (+.f64 (*.f64 x.re x.re) (*.f64 x.im x.im)))) y.im) (*.f64 (atan2.f64 x.im x.re) y.re)))
32.0b
(sqrt.f64 (+.f64 (*.f64 x.re x.re) (*.f64 x.im x.im)))
32.0b
(sqrt.f64 (+.f64 (*.f64 x.re x.re) (*.f64 x.im x.im)))

rewrite28.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt_binary64
*-un-lft-identity_binary64 pow1_binary64 add-cube-cbrt_binary64
add-exp-log_binary64 add-cbrt-cube_binary64 sqrt-prod_binary64
add-log-exp_binary64 sqrt-div_binary64
associate-*r*_binary64 associate-*l*_binary64
flip3-+_binary64 pow1/2_binary64 sqrt-pow1_binary64 rem-sqrt-square_binary64 flip-+_binary64
pow-prod-down_binary64 cbrt-unprod_binary64 sin-sum_binary64 unswap-sqr_binary64 prod-exp_binary64 *-commutative_binary64
Counts
4 → 56
Calls

8 calls:

6.0ms
(sin.f64 (+.f64 (*.f64 (log.f64 (sqrt.f64 (+.f64 (*.f64 x.re x.re) (*.f64 x.im x.im)))) y.im) (*.f64 (atan2.f64 x.im x.re) y.re)))
6.0ms
(sqrt.f64 (+.f64 (*.f64 x.re x.re) (*.f64 x.im x.im)))
4.0ms
(sqrt.f64 (+.f64 (*.f64 x.re x.re) (*.f64 x.im x.im)))
4.0ms
(*.f64 (atan2.f64 x.im x.re) y.im)
0.0ms
(+.f64 (*.f64 x.re x.re) (*.f64 x.im x.im))

series730.0ms (4.9%)

Counts
4 → 58
Calls

4 calls:

413.0ms
(sin.f64 (+.f64 (*.f64 (log.f64 (sqrt.f64 (+.f64 (*.f64 x.re x.re) (*.f64 x.im x.im)))) y.im) (*.f64 (atan2.f64 x.im x.re) y.re)))
138.0ms
(sqrt.f64 (+.f64 (*.f64 x.re x.re) (*.f64 x.im x.im)))
108.0ms
(sqrt.f64 (+.f64 (*.f64 x.re x.re) (*.f64 x.im x.im)))
71.0ms
(*.f64 (atan2.f64 x.im x.re) y.im)
Compiler

Compiled 4110 to 2665 computations (35.2% saved)

simplify83.0ms (0.6%)

Algorithm
egg-herbie
Counts
114 → 114
Iterations

Useful iterations: 0 (52.0ms)

IterNodesCost
050502475

prune233.0ms (1.6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New1068114
Fresh000
Picked011
Done000
Total1069115
Error
22.4b
Counts
115 → 9
Compiler

Compiled 5034 to 1393 computations (72.3% saved)

localize42.0ms (0.3%)

Local error

Found 8 expressions with local error:

0.0b
(+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2))
0.0b
(+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2))
0.0b
(+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2))
0.0b
(+.f64 (*.f64 x.re x.re) (*.f64 x.im x.im))
32.0b
(sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))
32.0b
(sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))
32.0b
(sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))
32.0b
(sqrt.f64 (+.f64 (*.f64 x.re x.re) (*.f64 x.im x.im)))

rewrite42.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
20×*-un-lft-identity_binary64
18×sqrt-prod_binary64
12×add-sqr-sqrt_binary64
pow1_binary64 add-cube-cbrt_binary64 sqrt-div_binary64
distribute-lft-out_binary64 unpow-prod-down_binary64
flip3-+_binary64 add-log-exp_binary64 pow1/2_binary64 add-exp-log_binary64 add-cbrt-cube_binary64 sqrt-pow1_binary64 rem-sqrt-square_binary64 flip-+_binary64
Counts
4 → 66
Calls

8 calls:

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

series601.0ms (4%)

Counts
4 → 62
Calls

4 calls:

155.0ms
(sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))
154.0ms
(sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))
154.0ms
(sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))
137.0ms
(sqrt.f64 (+.f64 (*.f64 x.re x.re) (*.f64 x.im x.im)))
Compiler

Compiled 7196 to 4762 computations (33.8% saved)

simplify69.0ms (0.5%)

Algorithm
egg-herbie
Counts
128 → 128
Iterations

Useful iterations: 0 (44.0ms)

IterNodesCost
050522209

prune479.0ms (3.2%)

Pruning

11 alts after pruning (9 fresh and 2 done)

PrunedKeptTotal
New1262128
Fresh077
Picked011
Done011
Total12611137
Error
22.4b
Counts
137 → 11
Compiler

Compiled 10882 to 5424 computations (50.2% saved)

localize31.0ms (0.2%)

Local error

Found 8 expressions with local error:

0.0b
(+.f64 (*.f64 (log.f64 (sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))) y.im) (*.f64 (atan2.f64 x.im x.re) y.re))
0.0b
(*.f64 (exp.f64 (-.f64 (*.f64 (log.f64 (sqrt.f64 (+.f64 (*.f64 x.re x.re) (*.f64 x.im x.im)))) y.re) (*.f64 (atan2.f64 x.im x.re) y.im))) (cbrt.f64 (pow.f64 (sin.f64 (+.f64 (*.f64 (log.f64 (sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))) y.im) (*.f64 (atan2.f64 x.im x.re) y.re))) 3)))
0.0b
(+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2))
0.0b
(+.f64 (*.f64 x.re x.re) (*.f64 x.im x.im))
14.3b
(cbrt.f64 (pow.f64 (sin.f64 (+.f64 (*.f64 (log.f64 (sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))) y.im) (*.f64 (atan2.f64 x.im x.re) y.re))) 3))
29.8b
(sin.f64 (+.f64 (*.f64 (log.f64 (sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))) y.im) (*.f64 (atan2.f64 x.im x.re) y.re)))
32.0b
(sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))
32.0b
(sqrt.f64 (+.f64 (*.f64 x.re x.re) (*.f64 x.im x.im)))

rewrite34.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
13×*-un-lft-identity_binary64
12×cbrt-prod_binary64
11×add-sqr-sqrt_binary64
add-cube-cbrt_binary64
sqrt-prod_binary64
pow1_binary64
unpow-prod-down_binary64
add-log-exp_binary64 add-exp-log_binary64 add-cbrt-cube_binary64 sqrt-div_binary64
cube-prod_binary64
flip3-+_binary64 pow1/2_binary64 distribute-lft-out_binary64 sqrt-pow1_binary64 rem-sqrt-square_binary64 flip-+_binary64
rem-cbrt-cube_binary64 pow1/3_binary64 sin-sum_binary64 sqr-pow_binary64 unpow3_binary64 cube-mult_binary64
Counts
4 → 61
Calls

8 calls:

8.0ms
(sin.f64 (+.f64 (*.f64 (log.f64 (sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))) y.im) (*.f64 (atan2.f64 x.im x.re) y.re)))
8.0ms
(sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))
5.0ms
(cbrt.f64 (pow.f64 (sin.f64 (+.f64 (*.f64 (log.f64 (sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))) y.im) (*.f64 (atan2.f64 x.im x.re) y.re))) 3))
4.0ms
(sqrt.f64 (+.f64 (*.f64 x.re x.re) (*.f64 x.im x.im)))
0.0ms
(+.f64 (*.f64 x.re x.re) (*.f64 x.im x.im))

series937.0ms (6.3%)

Counts
4 → 65
Calls

4 calls:

397.0ms
(cbrt.f64 (pow.f64 (sin.f64 (+.f64 (*.f64 (log.f64 (sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))) y.im) (*.f64 (atan2.f64 x.im x.re) y.re))) 3))
316.0ms
(sin.f64 (+.f64 (*.f64 (log.f64 (sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))) y.im) (*.f64 (atan2.f64 x.im x.re) y.re)))
116.0ms
(sqrt.f64 (+.f64 (pow.f64 x.re 2) (pow.f64 x.im 2)))
108.0ms
(sqrt.f64 (+.f64 (*.f64 x.re x.re) (*.f64 x.im x.im)))
Compiler

Compiled 4988 to 3451 computations (30.8% saved)

simplify110.0ms (0.7%)

Algorithm
egg-herbie
Counts
126 → 126
Iterations

Useful iterations: 0 (71.0ms)

IterNodesCost
049563742
149563742

prune271.0ms (1.8%)

Pruning

13 alts after pruning (11 fresh and 2 done)

PrunedKeptTotal
New1224126
Fresh178
Picked011
Done112
Total12413137
Error
22.4b
Counts
137 → 13
Compiler

Compiled 6131 to 2612 computations (57.4% saved)

localize26.0ms (0.2%)

Local error

Found 8 expressions with local error:

0.0b
(exp.f64 (-.f64 (*.f64 (log.f64 (sqrt.f64 (+.f64 (*.f64 x.re x.re) (*.f64 x.im x.im)))) y.re) (*.f64 (atan2.f64 x.im x.re) y.im)))
0.0b
(*.f64 (exp.f64 (-.f64 (*.f64 (log.f64 (sqrt.f64 (+.f64 (*.f64 x.re x.re) (*.f64 x.im x.im)))) y.re) (*.f64 (atan2.f64 x.im x.re) y.im))) (cbrt.f64 (pow.f64 (sin.f64 (*.f64 (atan2.f64 x.im x.re) y.re)) 3)))
0.0b
(-.f64 (*.f64 (log.f64 (sqrt.f64 (+.f64 (*.f64 x.re x.re) (*.f64 x.im x.im)))) y.re) (*.f64 (atan2.f64 x.im x.re) y.im))
0.0b
(+.f64 (*.f64 x.re x.re) (*.f64 x.im x.im))
1.5b
(*.f64 (atan2.f64 x.im x.re) y.im)
16.8b
(sin.f64 (*.f64 (atan2.f64 x.im x.re) y.re))
22.4b
(cbrt.f64 (pow.f64 (sin.f64 (*.f64 (atan2.f64 x.im x.re) y.re)) 3))
32.0b
(sqrt.f64 (+.f64 (*.f64 x.re x.re) (*.f64 x.im x.im)))

rewrite19.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt_binary64
12×cbrt-prod_binary64
10×*-un-lft-identity_binary64 add-cube-cbrt_binary64
pow1_binary64
add-exp-log_binary64 add-cbrt-cube_binary64
add-log-exp_binary64
associate-*r*_binary64 associate-*l*_binary64 unpow-prod-down_binary64 cube-prod_binary64 sqrt-prod_binary64
sqrt-div_binary64
pow-prod-down_binary64 flip3-+_binary64 pow1/2_binary64 rem-cbrt-cube_binary64 cbrt-unprod_binary64 pow1/3_binary64 sqr-pow_binary64 sqrt-pow1_binary64 unswap-sqr_binary64 rem-sqrt-square_binary64 prod-exp_binary64 flip-+_binary64 unpow3_binary64 *-commutative_binary64 cube-mult_binary64
Counts
4 → 61
Calls

8 calls:

4.0ms
(sqrt.f64 (+.f64 (*.f64 x.re x.re) (*.f64 x.im x.im)))
4.0ms
(*.f64 (atan2.f64 x.im x.re) y.im)
3.0ms
(cbrt.f64 (pow.f64 (sin.f64 (*.f64 (atan2.f64 x.im x.re) y.re)) 3))
2.0ms
(sin.f64 (*.f64 (atan2.f64 x.im x.re) y.re))
0.0ms
(+.f64 (*.f64 x.re x.re) (*.f64 x.im x.im))

series469.0ms (3.1%)

Counts
4 → 47
Calls

4 calls:

134.0ms
(sqrt.f64 (+.f64 (*.f64 x.re x.re) (*.f64 x.im x.im)))
134.0ms
(sin.f64 (*.f64 (atan2.f64 x.im x.re) y.re))
127.0ms
(cbrt.f64 (pow.f64 (sin.f64 (*.f64 (atan2.f64 x.im x.re) y.re)) 3))
73.0ms
(*.f64 (atan2.f64 x.im x.re) y.im)
Compiler

Compiled 2411 to 1747 computations (27.5% saved)

simplify75.0ms (0.5%)

Algorithm
egg-herbie
Counts
108 → 108
Iterations

Useful iterations: 0 (52.0ms)

IterNodesCost
050991719

prune138.0ms (0.9%)

Pruning

15 alts after pruning (13 fresh and 2 done)

PrunedKeptTotal
New1044108
Fresh1910
Picked101
Done022
Total10615121
Error
14.5b
Counts
121 → 15
Compiler

Compiled 3342 to 898 computations (73.1% saved)

simplify39.0ms (0.3%)

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (5.0ms)

IterNodesCost
02953068
12953068

regimes734.0ms (4.9%)

Compiler

Compiled 6316 to 4284 computations (32.2% saved)

bsearch364.0ms (2.4%)

Steps
ItersRangePoint
6
1.798301029127406e+54
7.925587002278094e+54
3.830449135996521e+54
9
279.84913426541436
930935118.0435365
72273.62012139842
7
4.329247734157589e-174
1.1560899359757212e-172
1.4724929191929907e-173
10
-8.991598433474235e-114
-3.20204909375144e-125
-7.152265036082887e-122
9
-1.3070488064622128e+146
-5.359028552902453e+138
-4.6754114793960554e+144
Compiler

Compiled 1 to 4 computations (-300% saved)

regimes268.0ms (1.8%)

Compiler

Compiled 1544 to 1132 computations (26.7% saved)

bsearch306.0ms (2%)

Steps
ItersRangePoint
8
1.068111152388603e-40
8.647073850089077e-38
1.501996167680406e-40
7
4.329247734157589e-174
1.1560899359757212e-172
3.94978284085457e-173
10
-8.991598433474235e-114
-3.20204909375144e-125
-5.321995205341738e-121
9
-1.3070488064622128e+146
-5.359028552902453e+138
-2.1801185610017876e+144
Compiler

Compiled 1 to 4 computations (-300% saved)

regimes271.0ms (1.8%)

Compiler

Compiled 1400 to 1056 computations (24.6% saved)

bsearch285.0ms (1.9%)

Steps
ItersRangePoint
8
1.068111152388603e-40
8.647073850089077e-38
5.880991632537931e-40
8
1.2330911022086788e-128
3.1264853859384725e-125
1.8088105277735776e-127
10
-7.847056780010913e-263
-4.703633979698483e-277
-1.552059420187445e-273
9
-1.3070488064622128e+146
-5.359028552902453e+138
-1.2831397775390236e+146
Compiler

Compiled 1 to 4 computations (-300% saved)

regimes237.0ms (1.6%)

Compiler

Compiled 1040 to 808 computations (22.3% saved)

bsearch260.0ms (1.7%)

Steps
ItersRangePoint
6
1.798301029127406e+54
7.925587002278094e+54
1.8236767072772018e+54
9
279.84913426541436
930935118.0435365
135259661.61043206
7
4.329247734157589e-174
1.1560899359757212e-172
1.144171802967284e-172
9
-1.362267226802697e+112
-1.6908110596238152e+106
-1.9683313878826213e+107
Compiler

Compiled 1 to 4 computations (-300% saved)

regimes176.0ms (1.2%)

Compiler

Compiled 680 to 568 computations (16.5% saved)

bsearch160.0ms (1.1%)

Steps
ItersRangePoint
9
-5.323087326817052e-305
3.84416746015919e-305
8.475330792296708e-308
9
-1.362267226802697e+112
-1.6908110596238152e+106
-1.0944590773690195e+108
Compiler

Compiled 1 to 4 computations (-300% saved)

regimes151.0ms (1%)

Compiler

Compiled 560 to 488 computations (12.9% saved)

bsearch313.0ms (2.1%)

Steps
ItersRangePoint
6
28.656547866029342
279.84913426541436
30.72037689046524
10
5.406658885496711e-105
9.36572646583306e-95
2.62250545672576e-102
5
4.829427398061274e-194
1.2999749633185382e-193
1.2755997546763125e-193
9
-1.362267226802697e+112
-1.6908110596238152e+106
-2.2693329803941562e+110
Compiler

Compiled 1 to 4 computations (-300% saved)

regimes123.0ms (0.8%)

Compiler

Compiled 384 to 352 computations (8.3% saved)

bsearch89.0ms (0.6%)

Steps
ItersRangePoint
4
0.0006698739119364151
0.0013094401609346986
0.0009212228530309738
9
-4.285748865682573e-15
-4.9209678054321526e-21
-5.6399303469765735e-21
Compiler

Compiled 1 to 4 computations (-300% saved)

regimes93.0ms (0.6%)

Compiler

Compiled 116 to 156 computations (-34.5% saved)

bsearch71.0ms (0.5%)

Steps
ItersRangePoint
4
0.0006698739119364151
0.0013094401609346986
0.0007733705347400569
9
-4.285748865682573e-15
-4.9209678054321526e-21
-3.177892013087221e-20
Compiler

Compiled 1 to 4 computations (-300% saved)

regimes34.0ms (0.2%)

Accuracy

Total 10.2b remaining (45.8%)

Threshold costs 0b (0%)

Compiler

Compiled 20 to 92 computations (-360% saved)

bsearch29.0ms (0.2%)

Compiler

Compiled 908 to 366 computations (59.7% saved)

simplify19.0ms (0.1%)

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (3.0ms)

IterNodesCost
02001733
12001733

end0.0ms (0%)

sample5.0s (33.3%)

Algorithm
intervals
Results
1.2s2429×body1024invalid
851.0ms7585×body128valid
319.0ms887×body512invalid
164.0ms193×body2048invalid
98.0ms188×body1024valid
76.0ms322×body256invalid
59.0ms509×body128invalid
44.0ms131×body512valid
19.0ms83×body256valid
10.0ms13×body2048valid
Compiler

Compiled 2503 to 1450 computations (42.1% saved)

Pareto

0.3053167431012725

Profiling

Loading profile data...