Details

analyze906.0ms (15.3%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	98
1	25	98
0	4	4
1	4	4

Search

True	Other	False	Iter
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
0%	99.8%	0.2%	8
6.2%	93.6%	0.2%	9
12.5%	87.3%	0.2%	10
25%	74.9%	0.2%	11
31.2%	63.9%	4.9%	12
39%	50.9%	10.1%	13
44.8%	44.4%	10.7%	14

Symmetry

(sort x.re y.im)

(sort x.im y.re)

Compiler

Compiled 8 to 8 computations (0% saved)

sample31.0ms (0.5%)

Algorithm

1×

intervals

Results

7.0ms	256×	body	128	valid
1.0ms	37×	body	128	invalid

Compiler

Compiled 15 to 19 computations (-26.7% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	13	14
1	13	14

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Error

0.0b

Counts

2 → 1

Compiler

Compiled 14 to 14 computations (0% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

0.0b	(+.f64 (.f64 x.re y.im) (.f64 x.im y.re))

rewrite13.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

3×	`add-log-exp_binary64_1140`
1×	`sum-log_binary64_1192` `pow1_binary64_1162` `add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137` `add-cube-cbrt_binary64_1136` `add-sqr-sqrt_binary64_1123` `flip3-+_binary64_1104` `*-un-lft-identity_binary64_1101` `flip-+_binary64_1075` `+-commutative_binary64_1031`

Counts

1 → 11

Calls

1 calls:

4.0ms

(+.f64 (*.f64 x.re y.im) (*.f64 x.im y.re))

Compiler

Compiled 178 to 42 computations (76.4% saved)

series149.0ms (2.5%)

Error

0.0b

Counts

1 → 24

Calls

1 calls:

139.0ms

(+.f64 (*.f64 x.re y.im) (*.f64 x.im y.re))

Compiler

Compiled 324 to 235 computations (27.5% saved)

simplify92.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

35 → 35

Iterations

Useful iterations: 0 (83.0ms)

Iter	Nodes	Cost
0	4833	489
1	4833	489

prune21.0ms (0.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	33	2	35
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	33	3	36

Error

0.0b

Counts

36 → 3

Compiler

Compiled 306 to 61 computations (80.1% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 y.re x.im) (.f64 y.im x.re))
0.2b	(.f64 (sqrt.f64 (+.f64 (.f64 y.re x.im) (.f64 y.im x.re))) (sqrt.f64 (+.f64 (.f64 y.re x.im) (*.f64 y.im x.re))))
1.3b	(sqrt.f64 (+.f64 (.f64 y.re x.im) (.f64 y.im x.re)))
1.3b	(sqrt.f64 (+.f64 (.f64 y.re x.im) (.f64 y.im x.re)))

rewrite119.0ms (2%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

30×	`add-sqr-sqrt_binary64_1123`
24×	`sqrt-prod_binary64_1117`
21×	`pow1_binary64_1162`
16×	`sqrt-div_binary64_1118`
14×	`add-cube-cbrt_binary64_1136` `*-un-lft-identity_binary64_1101`
10×	`pow1/2_binary64_1181` `sqrt-pow1_binary64_1119`
9×	`flip3-+_binary64_1104` `flip-+_binary64_1075`
8×	`swap-sqr_binary64_1068`
6×	`add-log-exp_binary64_1140` `add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137` `associate-l_binary64_1042` `associate-r_binary64_1041`
5×	`pow-prod-up_binary64_1171`
4×	`rem-sqrt-square_binary64_1114` `frac-times_binary64_1111` `unswap-sqr_binary64_1069`
3×	`pow-prod-down_binary64_1172` `pow-sqr_binary64_1074`
2×	`associate-l/_binary64_1044` `associate-r/_binary64_1043`
1×	`pow2_binary64_1182` `pow-plus_binary64_1164` `prod-exp_binary64_1150` `cbrt-unprod_binary64_1134` `sqrt-unprod_binary64_1121` `sqr-abs_binary64_1116` `rem-square-sqrt_binary64_1113` `*-commutative_binary64_1032` `sum-log_binary64_1192` `+-commutative_binary64_1031`

Counts

4 → 99

Calls

4 calls:

13.0ms	(.f64 (sqrt.f64 (+.f64 (.f64 y.re x.im) (.f64 y.im x.re))) (sqrt.f64 (+.f64 (.f64 y.re x.im) (*.f64 y.im x.re))))
7.0ms	(+.f64 (.f64 y.re x.im) (.f64 y.im x.re))
4.0ms	(sqrt.f64 (+.f64 (.f64 y.re x.im) (.f64 y.im x.re)))
4.0ms	(sqrt.f64 (+.f64 (.f64 y.re x.im) (.f64 y.im x.re)))

Compiler

Compiled 2841 to 323 computations (88.6% saved)

series491.0ms (8.3%)

Error

0.0b

Counts

4 → 80

Calls

4 calls:

123.0ms	(.f64 (sqrt.f64 (+.f64 (.f64 y.re x.im) (.f64 y.im x.re))) (sqrt.f64 (+.f64 (.f64 y.re x.im) (*.f64 y.im x.re))))
122.0ms	(+.f64 (.f64 y.re x.im) (.f64 y.im x.re))
107.0ms	(sqrt.f64 (+.f64 (.f64 y.re x.im) (.f64 y.im x.re)))
105.0ms	(sqrt.f64 (+.f64 (.f64 y.re x.im) (.f64 y.im x.re)))

Compiler

Compiled 3112 to 1668 computations (46.4% saved)

simplify105.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

179 → 179

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4917	3141
1	4917	3141

prune104.0ms (1.8%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	178	1	179
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	178	4	182

Error

0.0b

Counts

182 → 4

Compiler

Compiled 3073 to 391 computations (87.3% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 y.re x.im) (.f64 y.im x.re)))) (pow.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 y.im x.re) (*.f64 y.re x.im)))) 3))
0.3b	(pow.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 y.im x.re) (.f64 y.re x.im)))) 3)
1.3b	(sqrt.f64 (+.f64 (.f64 y.im x.re) (.f64 y.re x.im)))
1.3b	(sqrt.f64 (+.f64 (.f64 y.re x.im) (.f64 y.im x.re)))

rewrite212.0ms (3.6%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

93×	`sqrt-prod_binary64_1117`
70×	`add-sqr-sqrt_binary64_1123`
32×	`sqrt-div_binary64_1118`
27×	`unpow-prod-down_binary64_1180` `cube-prod_binary64_1129`
24×	`unswap-sqr_binary64_1069` `associate-r_binary64_1041`
23×	`add-cube-cbrt_binary64_1136` `*-un-lft-identity_binary64_1101`
10×	`add-exp-log_binary64_1139`
9×	`pow1_binary64_1162` `flip3-+_binary64_1104` `flip-+_binary64_1075` `associate-l_binary64_1042`
8×	`cube-div_binary64_1130`
7×	`add-cbrt-cube_binary64_1137`
6×	`sqrt-pow1_binary64_1119`
5×	`pow-pow_binary64_1173` `sqr-pow_binary64_1073`
4×	`pow1/2_binary64_1181` `add-log-exp_binary64_1140` `frac-times_binary64_1111`
3×	`pow-unpow_binary64_1178` `prod-exp_binary64_1150`
2×	`rem-sqrt-square_binary64_1114` `pow-to-exp_binary64_1170` `pow-exp_binary64_1169` `unpow3_binary64_1167` `cube-mult_binary64_1131` `associate-l/_binary64_1044` `associate-r/_binary64_1043`
1×	`rem-cube-cbrt_binary64_1124` `sqrt-pow2_binary64_1120` `cbrt-unprod_binary64_1134` `*-commutative_binary64_1032`

Counts

4 → 149

Calls

4 calls:

23.0ms	(.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 y.re x.im) (.f64 y.im x.re)))) (pow.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 y.im x.re) (*.f64 y.re x.im)))) 3))
7.0ms	(pow.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 y.im x.re) (.f64 y.re x.im)))) 3)
4.0ms	(sqrt.f64 (+.f64 (.f64 y.im x.re) (.f64 y.re x.im)))
4.0ms	(sqrt.f64 (+.f64 (.f64 y.re x.im) (.f64 y.im x.re)))

Compiler

Compiled 5473 to 1076 computations (80.3% saved)

series1.4s (23.6%)

Error

0.0b

Counts

4 → 80

Calls

4 calls:

839.0ms	(pow.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 y.im x.re) (.f64 y.re x.im)))) 3)
276.0ms	(.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 y.re x.im) (.f64 y.im x.re)))) (pow.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 y.im x.re) (*.f64 y.re x.im)))) 3))
110.0ms	(sqrt.f64 (+.f64 (.f64 y.re x.im) (.f64 y.im x.re)))
106.0ms	(sqrt.f64 (+.f64 (.f64 y.im x.re) (.f64 y.re x.im)))

Compiler

Compiled 5004 to 3405 computations (32% saved)

simplify116.0ms (2%)

Algorithm

1×	egg-herbie

Counts

229 → 229

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4951	5972
1	4951	5972

prune188.0ms (3.2%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	229	0	229
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	229	4	233

Error

0.0b

Counts

233 → 4

Compiler

Compiled 5459 to 1306 computations (76.1% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (.f64 y.re x.im) (.f64 y.im x.re))
0.3b	(pow.f64 (+.f64 (.f64 y.re x.im) (.f64 y.im x.re)) 3)
36.6b	(cbrt.f64 (pow.f64 (+.f64 (.f64 y.re x.im) (.f64 y.im x.re)) 3))

rewrite69.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Error

Rules

12×	`cbrt-prod_binary64_1132`
9×	`add-cube-cbrt_binary64_1136` `add-sqr-sqrt_binary64_1123` `*-un-lft-identity_binary64_1101`
6×	`unpow-prod-down_binary64_1180` `cube-prod_binary64_1129`
5×	`add-log-exp_binary64_1140`
4×	`pow1_binary64_1162` `add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137` `cube-div_binary64_1130`
3×	`flip3-+_binary64_1104` `flip-+_binary64_1075` `pow-unpow_binary64_1178`
2×	`cbrt-div_binary64_1133` `unpow3_binary64_1167` `cube-mult_binary64_1131` `sqr-pow_binary64_1073`
1×	`pow1/3_binary64_1183` `rem-cbrt-cube_binary64_1125` `pow-pow_binary64_1173` `pow-to-exp_binary64_1170` `pow-exp_binary64_1169` `rem-cube-cbrt_binary64_1124` `sum-log_binary64_1192` `+-commutative_binary64_1031`

Counts

3 → 59

Calls

3 calls:

5.0ms	(cbrt.f64 (pow.f64 (+.f64 (.f64 y.re x.im) (.f64 y.im x.re)) 3))
5.0ms	(pow.f64 (+.f64 (.f64 y.re x.im) (.f64 y.im x.re)) 3)
4.0ms	(+.f64 (.f64 y.re x.im) (.f64 y.im x.re))

Compiler

Compiled 1234 to 391 computations (68.3% saved)

series603.0ms (10.2%)

Error

0.0b

Counts

3 → 96

Calls

3 calls:

255.0ms	(pow.f64 (+.f64 (.f64 y.re x.im) (.f64 y.im x.re)) 3)
131.0ms	(+.f64 (.f64 y.re x.im) (.f64 y.im x.re))
129.0ms	(cbrt.f64 (pow.f64 (+.f64 (.f64 y.re x.im) (.f64 y.im x.re)) 3))

Compiler

Compiled 3468 to 2755 computations (20.6% saved)

simplify102.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

155 → 155

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	5303	3766

prune120.0ms (2%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	154	1	155
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	154	5	159

Error

Counts

159 → 5

Compiler

Compiled 2378 to 1066 computations (55.2% saved)

regimes188.0ms (3.2%)

Accuracy

Total 0.0b remaining (41.1%)

Threshold costs 0.0b (41.1%)

Compiler

Compiled 1966 to 1186 computations (39.7% saved)

bsearch0.0ms (0%)

simplify25.0ms (0.4%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	13	14
1	13	14

Remove

(sort x.im y.re)

(sort x.re y.im)

Compiler

Compiled 28 to 28 computations (0% saved)

end0.0ms (0%)

sample824.0ms (13.9%)

Algorithm

1×

intervals

Results

213.0ms	8000×	body	128	valid
36.0ms	1337×	body	128	invalid

Compiler

Compiled 291 to 179 computations (38.5% saved)

Details

analyze906.0ms (15.3%)

sample31.0ms (0.5%)

simplify7.0ms (0.1%)

prune2.0ms (0%)

localize5.0ms (0.1%)

rewrite13.0ms (0.2%)

series149.0ms (2.5%)

simplify92.0ms (1.6%)

prune21.0ms (0.3%)

localize8.0ms (0.1%)

rewrite119.0ms (2%)

series491.0ms (8.3%)

simplify105.0ms (1.8%)

prune104.0ms (1.8%)

localize12.0ms (0.2%)

rewrite212.0ms (3.6%)

series1.4s (23.6%)

simplify116.0ms (2%)

prune188.0ms (3.2%)

localize8.0ms (0.1%)

rewrite69.0ms (1.2%)

series603.0ms (10.2%)

simplify102.0ms (1.7%)

prune120.0ms (2%)

regimes188.0ms (3.2%)

bsearch0.0ms (0%)

simplify25.0ms (0.4%)

end0.0ms (0%)

sample824.0ms (13.9%)

Profiling