Details

analyze443.0ms (4%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
50%	50%	0.1%	3
50%	50%	0.1%	4
62.4%	37.5%	0.1%	5
62.4%	37.5%	0.1%	6
68.7%	31.2%	0.1%	7
68.7%	31.2%	0.1%	8
71.8%	28.1%	0.1%	9
71.8%	28.1%	0.1%	10
73.4%	26.5%	0.1%	11
73.4%	26.5%	0.1%	12
74.1%	25.8%	0.1%	13
74.1%	25.8%	0.1%	14

Compiler

Compiled 18 to 13 computations (27.8% saved)

sample1.8s (16.6%)

Symmetry

(sort re im)

Results

790.0ms	6213×	body	128	valid
354.0ms	600×	body	4096	valid
313.0ms	642×	body	2048	valid
170.0ms	423×	body	1024	valid
77.0ms	258×	body	512	valid
28.0ms	120×	body	256	valid

Compiler

Compiled 53 to 38 computations (28.3% saved)

simplify35.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

621×	`fma-neg_binary64`
394×	`fma-def_binary64`
332×	`rules-42_binary64`
322×	`rules-41_binary64`
315×	`rules-40_binary64`

Counts

1 → 2

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	13	15
1	81	15
2	247	15
3	889	12
4	779	12
5	15	12

prune4.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

49.6b

Counts

3 → 2

Alt Table

Status	Error	Program
	59.8b	(*.f64 1/2 (sqrt.f64 (fma.f64 2 (sqrt.f64 2) 2)))
▶	51.9b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re))))

Compiler

Compiled 79 to 64 computations (19% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 re re) (.f64 im im))
✓	0.2b	(sqrt.f64 (.f64 2 (+.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
✓	1.1b	(+.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
✓	31.5b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

series74.0ms (0.7%)

Counts

4 → 80

Calls

4 calls:

42.0ms	(sqrt.f64 (.f64 2 (+.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
13.0ms	(+.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
12.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
8.0ms	(+.f64 (.f64 re re) (.f64 im im))

rewrite77.0ms (0.7%)

Algorithm

2×	batch-egg-rewrite

Rules

973×	`prod-diff_binary64`
168×	`egg-rr`
114×	`add-sqr-sqrt_binary64`
113×	`log1p-expm1-u_binary64`
113×	`expm1-log1p-u_binary64`

Counts

4 → 168

Calls

4 calls:

74.0ms	(+.f64 (.f64 re re) (.f64 im im))
74.0ms	(sqrt.f64 (.f64 2 (+.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
74.0ms	(+.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
74.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	31
1	274	30
2	3347	30
3	5110	30
0	0	0
1	0	0

simplify76.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

479×	`rules-21_binary64`
319×	`fma-neg_binary64`
277×	`rules-7-rev_binary64`
224×	`fma-def_binary64`
216×	`rules-20_binary64`

Counts

248 → 245

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	139	1555
1	967	1430
2	4338	1430
3	5033	1430

prune207.0ms (1.9%)

Pruning

26 alts after pruning (26 fresh and 0 done)

	Pruned	Kept	Total
New	220	25	245
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	221	26	247

Error

32.9b

Counts

247 → 26

Alt Table

Status	Error	Program
	59.8b	(*.f64 1/2 (sqrt.f64 (fma.f64 2 (sqrt.f64 2) 2)))
	53.3b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 (exp.f64 (*.f64 (log.f64 (pow.f64 (hypot.f64 re im) 2)) 1/2)) re))))
	41.5b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 (pow.f64 (sqrt.f64 (hypot.f64 re im)) 2) re))))
	43.2b	(.f64 1/2 (.f64 (sqrt.f64 2) (sqrt.f64 im)))
	58.9b	(.f64 1/2 (log.f64 (exp.f64 (sqrt.f64 (.f64 (+.f64 re (hypot.f64 re im)) 2)))))
	42.3b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 (pow.f64 (cbrt.f64 (hypot.f64 re im)) 3) re))))
	45.4b	(.f64 1/2 (-.f64 (exp.f64 (log1p.f64 (sqrt.f64 (.f64 (+.f64 re (hypot.f64 re im)) 2)))) 1))
	56.8b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 (pow.f64 (pow.f64 (hypot.f64 re im) 3) 1/3) re))))
	54.4b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 -1/2 (/.f64 (pow.f64 im 2) re)))))
	40.4b	(.f64 1/2 (pow.f64 (cbrt.f64 (sqrt.f64 (.f64 (+.f64 re (hypot.f64 re im)) 2))) 3))
	56.0b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 (/.f64 (pow.f64 (hypot.f64 re im) 3) (+.f64 (pow.f64 (hypot.f64 re im) 2) (+.f64 0 (*.f64 (hypot.f64 re im) 0)))) re))))
	45.5b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 (*.f64 1/2 (/.f64 (pow.f64 re 2) im)) (+.f64 re im)))))
	48.0b	(.f64 1/2 (pow.f64 (pow.f64 (.f64 (+.f64 re (hypot.f64 re im)) 2) 3/2) 1/3))
	41.8b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 (sqrt.f64 (hypot.f64 re im)) (+.f64 (sqrt.f64 (hypot.f64 re im)) (/.f64 re (sqrt.f64 (hypot.f64 re im))))))))
	63.9b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 (-.f64 (.f64 1/8 (/.f64 (pow.f64 re 4) (pow.f64 im 3))) (fma.f64 1/2 (/.f64 (.f64 re re) im) (fma.f64 1/16 (/.f64 (pow.f64 re 6) (pow.f64 im 5)) im))) re))))
	53.1b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 (sqrt.f64 (expm1.f64 (log1p.f64 (pow.f64 (hypot.f64 re im) 2)))) re))))
	42.5b	(.f64 1/2 (sqrt.f64 (.f64 2 (fma.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)) re))))
	42.3b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 (pow.f64 (cbrt.f64 (hypot.f64 re im)) 2) (+.f64 (cbrt.f64 (hypot.f64 re im)) (/.f64 re (pow.f64 (cbrt.f64 (hypot.f64 re im)) 2)))))))
	44.0b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 (pow.f64 (cbrt.f64 re) 2) (+.f64 (cbrt.f64 re) (/.f64 (hypot.f64 re im) (pow.f64 (cbrt.f64 re) 2)))))))
	42.3b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 (*.f64 (pow.f64 (cbrt.f64 (hypot.f64 re im)) 2) (cbrt.f64 (hypot.f64 re im))) re))))
▶	40.3b	(.f64 1/2 (.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (.f64 (+.f64 re (hypot.f64 re im)) 2)) 2)) (sqrt.f64 (cbrt.f64 (.f64 (+.f64 re (hypot.f64 re im)) 2)))))
	42.8b	(.f64 1/2 (sqrt.f64 (.f64 2 (fma.f64 (pow.f64 (cbrt.f64 (hypot.f64 re im)) 2) (cbrt.f64 (hypot.f64 re im)) re))))
	48.4b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 (-.f64 (exp.f64 (log1p.f64 (hypot.f64 re im))) 1) re))))
	42.2b	(.f64 1/2 (sqrt.f64 (.f64 2 (fma.f64 (pow.f64 (cbrt.f64 re) 2) (cbrt.f64 re) (hypot.f64 re im)))))
	42.6b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 re (+.f64 1 (/.f64 (hypot.f64 re im) re))))))
	43.4b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 (expm1.f64 (log1p.f64 (hypot.f64 re im))) re))))

Compiler

Compiled 5631 to 3775 computations (33% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (.f64 (+.f64 re (hypot.f64 re im)) 2)) 2)) (sqrt.f64 (cbrt.f64 (*.f64 (+.f64 re (hypot.f64 re im)) 2))))
✓	0.2b	(pow.f64 (cbrt.f64 (*.f64 (+.f64 re (hypot.f64 re im)) 2)) 2)
✓	0.5b	(cbrt.f64 (*.f64 (+.f64 re (hypot.f64 re im)) 2))
✓	1.1b	(+.f64 re (hypot.f64 re im))

series194.0ms (1.8%)

Counts

4 → 80

Calls

4 calls:

95.0ms	(pow.f64 (cbrt.f64 (*.f64 (+.f64 re (hypot.f64 re im)) 2)) 2)
53.0ms	(cbrt.f64 (*.f64 (+.f64 re (hypot.f64 re im)) 2))
34.0ms	(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (.f64 (+.f64 re (hypot.f64 re im)) 2)) 2)) (sqrt.f64 (cbrt.f64 (*.f64 (+.f64 re (hypot.f64 re im)) 2))))
11.0ms	(+.f64 re (hypot.f64 re im))

rewrite100.0ms (0.9%)

Algorithm

2×	batch-egg-rewrite

Rules

862×	`fma-neg_binary64`
517×	`prod-diff_binary64`
308×	`egg-rr`
178×	`expm1-udef_binary64`
178×	`log1p-udef_binary64`

Counts

4 → 308

Calls

4 calls:

93.0ms	(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (.f64 (+.f64 re (hypot.f64 re im)) 2)) 2)) (sqrt.f64 (cbrt.f64 (*.f64 (+.f64 re (hypot.f64 re im)) 2))))
93.0ms	(pow.f64 (cbrt.f64 (*.f64 (+.f64 re (hypot.f64 re im)) 2)) 2)
93.0ms	(cbrt.f64 (*.f64 (+.f64 re (hypot.f64 re im)) 2))
93.0ms	(+.f64 re (hypot.f64 re im))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	46
1	258	44
2	2948	44
3	5122	44
0	0	0
1	0	0

simplify95.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

896×	`fma-neg_binary64`
653×	`rules-20_binary64`
579×	`rules-41_binary64`
579×	`rules-43_binary64`
577×	`rules-40_binary64`

Counts

388 → 430

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	336	3760
1	2468	3760
2	5310	3760

prune750.0ms (6.8%)

Pruning

28 alts after pruning (28 fresh and 0 done)

	Pruned	Kept	Total
New	634	8	642
Fresh	5	20	25
Picked	1	0	1
Done	0	0	0
Total	640	28	668

Error

32.9b

Counts

668 → 28

Alt Table

Status	Error	Program
	48.0b	(.f64 1/2 (pow.f64 (pow.f64 (sqrt.f64 (.f64 (+.f64 re (hypot.f64 re im)) 2)) 3) 1/3))
	41.5b	(.f64 1/2 (pow.f64 (pow.f64 (.f64 (+.f64 re (hypot.f64 re im)) 2) 1/6) 3))
	42.6b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 re (+.f64 1 (/.f64 (hypot.f64 re im) re))))))
	59.8b	(*.f64 1/2 (sqrt.f64 (fma.f64 2 (sqrt.f64 2) 2)))
	53.3b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 (exp.f64 (*.f64 (log.f64 (pow.f64 (hypot.f64 re im) 2)) 1/2)) re))))
	41.5b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 (pow.f64 (sqrt.f64 (hypot.f64 re im)) 2) re))))
	43.2b	(.f64 1/2 (.f64 (sqrt.f64 2) (sqrt.f64 im)))
	56.8b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 (pow.f64 (pow.f64 (hypot.f64 re im) 3) 1/3) re))))
	45.3b	(.f64 1/2 (.f64 (sqrt.f64 (pow.f64 (/.f64 (.f64 (+.f64 re (hypot.f64 re im)) 2) (+.f64 (pow.f64 (.f64 (+.f64 re (hypot.f64 re im)) 2) 2/3) (+.f64 0 (.f64 (cbrt.f64 (.f64 (+.f64 re (hypot.f64 re im)) 2)) 0)))) 2)) (sqrt.f64 (cbrt.f64 (*.f64 (+.f64 re (hypot.f64 re im)) 2)))))
	45.4b	(.f64 1/2 (-.f64 (exp.f64 (log1p.f64 (sqrt.f64 (.f64 (+.f64 re (hypot.f64 re im)) 2)))) 1))
	54.4b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 -1/2 (/.f64 (pow.f64 im 2) re)))))
	56.0b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 (/.f64 (pow.f64 (hypot.f64 re im) 3) (+.f64 (pow.f64 (hypot.f64 re im) 2) (+.f64 0 (*.f64 (hypot.f64 re im) 0)))) re))))
▶	41.3b	(.f64 1/2 (.f64 (sqrt.f64 (pow.f64 (exp.f64 (.f64 (log.f64 (pow.f64 (.f64 (+.f64 re (hypot.f64 re im)) 2) 2/3)) 1/2)) 2)) (sqrt.f64 (cbrt.f64 (*.f64 (+.f64 re (hypot.f64 re im)) 2)))))
	51.3b	(.f64 1/2 (.f64 (sqrt.f64 (pow.f64 (-.f64 (fma.f64 1/18 (.f64 (.f64 (.f64 re re) (cbrt.f64 2)) (cbrt.f64 (/.f64 -1 (pow.f64 im 5)))) (fma.f64 (cbrt.f64 (.f64 im -1)) (cbrt.f64 2) (.f64 4/81 (.f64 (.f64 (pow.f64 re 3) (cbrt.f64 2)) (cbrt.f64 (/.f64 -1 (pow.f64 im 8))))))) (.f64 1/3 (.f64 (.f64 re (cbrt.f64 2)) (cbrt.f64 (/.f64 -1 (.f64 im im)))))) 2)) (sqrt.f64 (cbrt.f64 (.f64 (+.f64 re (hypot.f64 re im)) 2)))))
	41.8b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 (sqrt.f64 (hypot.f64 re im)) (+.f64 (sqrt.f64 (hypot.f64 re im)) (/.f64 re (sqrt.f64 (hypot.f64 re im))))))))
	53.1b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 (sqrt.f64 (expm1.f64 (log1p.f64 (pow.f64 (hypot.f64 re im) 2)))) re))))
	42.5b	(.f64 1/2 (sqrt.f64 (.f64 2 (fma.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)) re))))
	42.3b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 (pow.f64 (cbrt.f64 (hypot.f64 re im)) 2) (+.f64 (cbrt.f64 (hypot.f64 re im)) (/.f64 re (pow.f64 (cbrt.f64 (hypot.f64 re im)) 2)))))))
	45.6b	(.f64 1/2 (.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (.f64 (-.f64 re (fma.f64 1/2 (/.f64 (.f64 re re) im) im)) 2)) 2)) (sqrt.f64 (cbrt.f64 (*.f64 (+.f64 re (hypot.f64 re im)) 2)))))
	45.6b	(.f64 1/2 (.f64 (sqrt.f64 (-.f64 (exp.f64 (log1p.f64 (pow.f64 (.f64 (+.f64 re (hypot.f64 re im)) 2) 2/3))) 1)) (sqrt.f64 (cbrt.f64 (.f64 (+.f64 re (hypot.f64 re im)) 2)))))
	44.0b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 (pow.f64 (cbrt.f64 re) 2) (+.f64 (cbrt.f64 re) (/.f64 (hypot.f64 re im) (pow.f64 (cbrt.f64 re) 2)))))))
	42.3b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 (*.f64 (pow.f64 (cbrt.f64 (hypot.f64 re im)) 2) (cbrt.f64 (hypot.f64 re im))) re))))
	46.3b	(.f64 1/2 (.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (.f64 (+.f64 re (hypot.f64 re im)) 2)) 2)) (sqrt.f64 (.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (.f64 (+.f64 re (hypot.f64 re im)) 2)) 4))) (sqrt.f64 (cbrt.f64 (pow.f64 (.f64 (+.f64 re (hypot.f64 re im)) 2) 2/3)))))))
	42.8b	(.f64 1/2 (sqrt.f64 (.f64 2 (fma.f64 (pow.f64 (cbrt.f64 (hypot.f64 re im)) 2) (cbrt.f64 (hypot.f64 re im)) re))))
	48.4b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 (-.f64 (exp.f64 (log1p.f64 (hypot.f64 re im))) 1) re))))
	42.2b	(.f64 1/2 (sqrt.f64 (.f64 2 (fma.f64 (pow.f64 (cbrt.f64 re) 2) (cbrt.f64 re) (hypot.f64 re im)))))
	43.4b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 (expm1.f64 (log1p.f64 (hypot.f64 re im))) re))))
	42.3b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 (pow.f64 (cbrt.f64 (hypot.f64 re im)) 3) re))))

Compiler

Compiled 26417 to 16900 computations (36% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.5b	(cbrt.f64 (*.f64 (+.f64 re (hypot.f64 re im)) 2))
	1.1b	(+.f64 re (hypot.f64 re im))
✓	2.2b	(exp.f64 (.f64 (log.f64 (pow.f64 (.f64 (+.f64 re (hypot.f64 re im)) 2) 2/3)) 1/2))
✓	3.4b	(pow.f64 (*.f64 (+.f64 re (hypot.f64 re im)) 2) 2/3)

series101.0ms (0.9%)

Counts

2 → 48

Calls

2 calls:

64.0ms	(exp.f64 (.f64 (log.f64 (pow.f64 (.f64 (+.f64 re (hypot.f64 re im)) 2) 2/3)) 1/2))
36.0ms	(pow.f64 (*.f64 (+.f64 re (hypot.f64 re im)) 2) 2/3)

rewrite72.0ms (0.7%)

Algorithm

2×	batch-egg-rewrite

Rules

490×	`prod-diff_binary64`
218×	`expm1-udef_binary64`
218×	`log1p-udef_binary64`
126×	`log1p-expm1-u_binary64`
126×	`expm1-log1p-u_binary64`

Counts

2 → 89

Calls

2 calls:

70.0ms	(exp.f64 (.f64 (log.f64 (pow.f64 (.f64 (+.f64 re (hypot.f64 re im)) 2) 2/3)) 1/2))
70.0ms	(pow.f64 (*.f64 (+.f64 re (hypot.f64 re im)) 2) 2/3)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	29
1	308	25
2	3483	25
3	4959	25
0	0	0
1	0	0

simplify64.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

618×	`fma-neg_binary64`
461×	`rules-20_binary64`
417×	`rules-41_binary64`
417×	`rules-43_binary64`
415×	`rules-40_binary64`

Counts

137 → 183

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	262	2547
1	1851	2481
2	5172	2481

prune637.0ms (5.8%)

Pruning

31 alts after pruning (31 fresh and 0 done)

	Pruned	Kept	Total
New	481	5	486
Fresh	1	26	27
Picked	1	0	1
Done	0	0	0
Total	483	31	514

Error

32.9b

Counts

514 → 31

Alt Table

Status	Error	Program
	41.5b	(.f64 1/2 (pow.f64 (pow.f64 (.f64 (+.f64 re (hypot.f64 re im)) 2) 1/6) 3))
	42.6b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 re (+.f64 1 (/.f64 (hypot.f64 re im) re))))))
	59.8b	(*.f64 1/2 (sqrt.f64 (fma.f64 2 (sqrt.f64 2) 2)))
	53.3b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 (exp.f64 (*.f64 (log.f64 (pow.f64 (hypot.f64 re im) 2)) 1/2)) re))))
	43.4b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 (expm1.f64 (log1p.f64 (hypot.f64 re im))) re))))
	50.3b	(.f64 1/2 (.f64 (sqrt.f64 (pow.f64 (pow.f64 (exp.f64 (sqrt.f64 (log.f64 (cbrt.f64 (.f64 (+.f64 re (hypot.f64 re im)) 2))))) (sqrt.f64 (log.f64 (cbrt.f64 (.f64 (+.f64 re (hypot.f64 re im)) 2))))) 2)) (sqrt.f64 (cbrt.f64 (*.f64 (+.f64 re (hypot.f64 re im)) 2)))))
	41.5b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 (pow.f64 (sqrt.f64 (hypot.f64 re im)) 2) re))))
	41.8b	(.f64 1/2 (.f64 (sqrt.f64 (pow.f64 (pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (cbrt.f64 (.f64 (+.f64 re (hypot.f64 re im)) 2)))) 2)) (cbrt.f64 (log.f64 (cbrt.f64 (.f64 (+.f64 re (hypot.f64 re im)) 2))))) 2)) (sqrt.f64 (cbrt.f64 (*.f64 (+.f64 re (hypot.f64 re im)) 2)))))
	43.2b	(.f64 1/2 (.f64 (sqrt.f64 2) (sqrt.f64 im)))
▶	41.4b	(.f64 1/2 (.f64 (sqrt.f64 (pow.f64 (exp.f64 (.f64 (log.f64 (pow.f64 (.f64 (+.f64 re (hypot.f64 re im)) 2) 2/3)) 1/2)) 2)) (sqrt.f64 (exp.f64 (.f64 (log.f64 (pow.f64 (.f64 (+.f64 re (hypot.f64 re im)) 2) 2/3)) 1/2)))))
	42.3b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 (pow.f64 (cbrt.f64 (hypot.f64 re im)) 3) re))))
	56.8b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 (pow.f64 (pow.f64 (hypot.f64 re im) 3) 1/3) re))))
	45.3b	(.f64 1/2 (.f64 (sqrt.f64 (pow.f64 (/.f64 (.f64 (+.f64 re (hypot.f64 re im)) 2) (+.f64 (pow.f64 (.f64 (+.f64 re (hypot.f64 re im)) 2) 2/3) (+.f64 0 (.f64 (cbrt.f64 (.f64 (+.f64 re (hypot.f64 re im)) 2)) 0)))) 2)) (sqrt.f64 (cbrt.f64 (*.f64 (+.f64 re (hypot.f64 re im)) 2)))))
	45.4b	(.f64 1/2 (-.f64 (exp.f64 (log1p.f64 (sqrt.f64 (.f64 (+.f64 re (hypot.f64 re im)) 2)))) 1))
	54.4b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 -1/2 (/.f64 (pow.f64 im 2) re)))))
	51.3b	(.f64 1/2 (.f64 (sqrt.f64 (pow.f64 (-.f64 (fma.f64 1/18 (.f64 (.f64 (.f64 re re) (cbrt.f64 2)) (cbrt.f64 (/.f64 -1 (pow.f64 im 5)))) (fma.f64 (cbrt.f64 (.f64 im -1)) (cbrt.f64 2) (.f64 4/81 (.f64 (.f64 (pow.f64 re 3) (cbrt.f64 2)) (cbrt.f64 (/.f64 -1 (pow.f64 im 8))))))) (.f64 1/3 (.f64 (.f64 re (cbrt.f64 2)) (cbrt.f64 (/.f64 -1 (.f64 im im)))))) 2)) (sqrt.f64 (cbrt.f64 (.f64 (+.f64 re (hypot.f64 re im)) 2)))))
	41.8b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 (sqrt.f64 (hypot.f64 re im)) (+.f64 (sqrt.f64 (hypot.f64 re im)) (/.f64 re (sqrt.f64 (hypot.f64 re im))))))))
	53.1b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 (sqrt.f64 (expm1.f64 (log1p.f64 (pow.f64 (hypot.f64 re im) 2)))) re))))
	42.5b	(.f64 1/2 (sqrt.f64 (.f64 2 (fma.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)) re))))
	42.3b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 (pow.f64 (cbrt.f64 (hypot.f64 re im)) 2) (+.f64 (cbrt.f64 (hypot.f64 re im)) (/.f64 re (pow.f64 (cbrt.f64 (hypot.f64 re im)) 2)))))))
	42.3b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 (*.f64 (pow.f64 (cbrt.f64 (hypot.f64 re im)) 2) (cbrt.f64 (hypot.f64 re im))) re))))
	54.1b	(.f64 1/2 (.f64 (sqrt.f64 (pow.f64 (exp.f64 (.f64 (log.f64 (/.f64 (pow.f64 (.f64 (+.f64 re (hypot.f64 re im)) 2) 2) (+.f64 (pow.f64 (.f64 (+.f64 re (hypot.f64 re im)) 2) 4/3) (+.f64 0 (.f64 (pow.f64 (.f64 (+.f64 re (hypot.f64 re im)) 2) 2/3) 0))))) 1/2)) 2)) (sqrt.f64 (cbrt.f64 (.f64 (+.f64 re (hypot.f64 re im)) 2)))))
	45.6b	(.f64 1/2 (.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (.f64 (-.f64 re (fma.f64 1/2 (/.f64 (.f64 re re) im) im)) 2)) 2)) (sqrt.f64 (cbrt.f64 (*.f64 (+.f64 re (hypot.f64 re im)) 2)))))
	45.6b	(.f64 1/2 (.f64 (sqrt.f64 (-.f64 (exp.f64 (log1p.f64 (pow.f64 (.f64 (+.f64 re (hypot.f64 re im)) 2) 2/3))) 1)) (sqrt.f64 (cbrt.f64 (.f64 (+.f64 re (hypot.f64 re im)) 2)))))
	44.0b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 (pow.f64 (cbrt.f64 re) 2) (+.f64 (cbrt.f64 re) (/.f64 (hypot.f64 re im) (pow.f64 (cbrt.f64 re) 2)))))))
	46.3b	(.f64 1/2 (.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (.f64 (+.f64 re (hypot.f64 re im)) 2)) 2)) (sqrt.f64 (.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (.f64 (+.f64 re (hypot.f64 re im)) 2)) 4))) (sqrt.f64 (cbrt.f64 (pow.f64 (.f64 (+.f64 re (hypot.f64 re im)) 2) 2/3)))))))
	42.8b	(.f64 1/2 (sqrt.f64 (.f64 2 (fma.f64 (pow.f64 (cbrt.f64 (hypot.f64 re im)) 2) (cbrt.f64 (hypot.f64 re im)) re))))
	48.4b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 (-.f64 (exp.f64 (log1p.f64 (hypot.f64 re im))) 1) re))))
	42.2b	(.f64 1/2 (sqrt.f64 (.f64 2 (fma.f64 (pow.f64 (cbrt.f64 re) 2) (cbrt.f64 re) (hypot.f64 re im)))))
	41.4b	(.f64 1/2 (.f64 (sqrt.f64 (pow.f64 (exp.f64 (.f64 (log.f64 (.f64 (pow.f64 (pow.f64 (.f64 (+.f64 re (hypot.f64 re im)) 2) 2/3) 2/3) (pow.f64 (cbrt.f64 (.f64 (+.f64 re (hypot.f64 re im)) 2)) 2/3))) 1/2)) 2)) (sqrt.f64 (cbrt.f64 (*.f64 (+.f64 re (hypot.f64 re im)) 2)))))
	56.0b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 (/.f64 (pow.f64 (hypot.f64 re im) 3) (+.f64 (pow.f64 (hypot.f64 re im) 2) (+.f64 0 (*.f64 (hypot.f64 re im) 0)))) re))))

Compiler

Compiled 22421 to 15374 computations (31.4% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(pow.f64 (exp.f64 (.f64 (log.f64 (pow.f64 (.f64 (+.f64 re (hypot.f64 re im)) 2) 2/3)) 1/2)) 2)
	1.1b	(+.f64 re (hypot.f64 re im))
	2.2b	(exp.f64 (.f64 (log.f64 (pow.f64 (.f64 (+.f64 re (hypot.f64 re im)) 2) 2/3)) 1/2))
	3.4b	(pow.f64 (*.f64 (+.f64 re (hypot.f64 re im)) 2) 2/3)

series85.0ms (0.8%)

Counts

1 → 24

Calls

1 calls:

85.0ms

(pow.f64 (exp.f64 (*.f64 (log.f64 (pow.f64 (*.f64 (+.f64 re (hypot.f64 re im)) 2) 2/3)) 1/2)) 2)

rewrite67.0ms (0.6%)

Algorithm

2×	batch-egg-rewrite

Rules

490×	`prod-diff_binary64`
220×	`expm1-udef_binary64`
220×	`log1p-udef_binary64`
135×	`log1p-expm1-u_binary64`
135×	`expm1-log1p-u_binary64`

Counts

1 → 51

Calls

1 calls:

65.0ms

(pow.f64 (exp.f64 (*.f64 (log.f64 (pow.f64 (*.f64 (+.f64 re (hypot.f64 re im)) 2) 2/3)) 1/2)) 2)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	19
1	332	13
2	3496	13
3	4962	13
0	0	0
1	0	0

simplify117.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

410×	`rules-21_binary64`
346×	`fma-neg_binary64`
252×	`rules-7-rev_binary64`
248×	`rules-20_binary64`
233×	`rules-41_binary64`

Counts

75 → 99

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	150	1408
1	1041	1328
2	4493	1214
3	4951	1131
4	4997	1131
5	4845	1131

prune830.0ms (7.5%)

Pruning

34 alts after pruning (33 fresh and 1 done)

	Pruned	Kept	Total
New	640	7	647
Fresh	4	26	30
Picked	0	1	1
Done	0	0	0
Total	644	34	678

Error

32.9b

Counts

678 → 34

Alt Table

Status	Error	Program
	59.8b	(*.f64 1/2 (sqrt.f64 (fma.f64 2 (sqrt.f64 2) 2)))
	53.3b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 (exp.f64 (*.f64 (log.f64 (pow.f64 (hypot.f64 re im) 2)) 1/2)) re))))
	43.4b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 (expm1.f64 (log1p.f64 (hypot.f64 re im))) re))))
	50.3b	(.f64 1/2 (.f64 (sqrt.f64 (pow.f64 (pow.f64 (exp.f64 (sqrt.f64 (log.f64 (cbrt.f64 (.f64 (+.f64 re (hypot.f64 re im)) 2))))) (sqrt.f64 (log.f64 (cbrt.f64 (.f64 (+.f64 re (hypot.f64 re im)) 2))))) 2)) (sqrt.f64 (cbrt.f64 (*.f64 (+.f64 re (hypot.f64 re im)) 2)))))
	41.5b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 (pow.f64 (sqrt.f64 (hypot.f64 re im)) 2) re))))
	41.8b	(.f64 1/2 (.f64 (sqrt.f64 (pow.f64 (pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (cbrt.f64 (.f64 (+.f64 re (hypot.f64 re im)) 2)))) 2)) (cbrt.f64 (log.f64 (cbrt.f64 (.f64 (+.f64 re (hypot.f64 re im)) 2))))) 2)) (sqrt.f64 (cbrt.f64 (*.f64 (+.f64 re (hypot.f64 re im)) 2)))))
	43.2b	(.f64 1/2 (.f64 (sqrt.f64 2) (sqrt.f64 im)))
✓	41.4b	(.f64 1/2 (.f64 (sqrt.f64 (pow.f64 (exp.f64 (.f64 (log.f64 (pow.f64 (.f64 (+.f64 re (hypot.f64 re im)) 2) 2/3)) 1/2)) 2)) (sqrt.f64 (exp.f64 (.f64 (log.f64 (pow.f64 (.f64 (+.f64 re (hypot.f64 re im)) 2) 2/3)) 1/2)))))
	42.3b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 (pow.f64 (cbrt.f64 (hypot.f64 re im)) 3) re))))
	63.9b	(.f64 1/2 (.f64 (sqrt.f64 (pow.f64 (-.f64 (fma.f64 1/18 (/.f64 (.f64 (.f64 re re) (exp.f64 (.f64 1/3 (-.f64 (log.f64 2) (log.f64 (/.f64 -1 im)))))) (.f64 im im)) (fma.f64 4/81 (/.f64 (.f64 (pow.f64 re 3) (exp.f64 (.f64 1/3 (-.f64 (log.f64 2) (log.f64 (/.f64 -1 im)))))) (pow.f64 im 3)) (exp.f64 (.f64 1/3 (-.f64 (log.f64 2) (log.f64 (/.f64 -1 im))))))) (.f64 1/3 (/.f64 (.f64 re (exp.f64 (.f64 1/3 (-.f64 (log.f64 2) (log.f64 (/.f64 -1 im)))))) im))) 2)) (sqrt.f64 (exp.f64 (.f64 (log.f64 (pow.f64 (.f64 (+.f64 re (hypot.f64 re im)) 2) 2/3)) 1/2)))))
	56.8b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 (pow.f64 (pow.f64 (hypot.f64 re im) 3) 1/3) re))))
	45.3b	(.f64 1/2 (.f64 (sqrt.f64 (pow.f64 (/.f64 (.f64 (+.f64 re (hypot.f64 re im)) 2) (+.f64 (pow.f64 (.f64 (+.f64 re (hypot.f64 re im)) 2) 2/3) (+.f64 0 (.f64 (cbrt.f64 (.f64 (+.f64 re (hypot.f64 re im)) 2)) 0)))) 2)) (sqrt.f64 (cbrt.f64 (*.f64 (+.f64 re (hypot.f64 re im)) 2)))))
	54.4b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 -1/2 (/.f64 (pow.f64 im 2) re)))))
	45.2b	(.f64 1/2 (.f64 (sqrt.f64 (pow.f64 (/.f64 (.f64 (+.f64 re (hypot.f64 re im)) 2) (+.f64 (pow.f64 (.f64 (+.f64 re (hypot.f64 re im)) 2) 2/3) (-.f64 0 (.f64 (cbrt.f64 (.f64 (+.f64 re (hypot.f64 re im)) 2)) 0)))) 2)) (sqrt.f64 (exp.f64 (.f64 (log.f64 (pow.f64 (.f64 (+.f64 re (hypot.f64 re im)) 2) 2/3)) 1/2)))))
	45.4b	(.f64 1/2 (-.f64 (exp.f64 (log1p.f64 (sqrt.f64 (.f64 (+.f64 re (hypot.f64 re im)) 2)))) 1))
	53.1b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 (sqrt.f64 (expm1.f64 (log1p.f64 (pow.f64 (hypot.f64 re im) 2)))) re))))
	42.5b	(.f64 1/2 (sqrt.f64 (.f64 2 (fma.f64 (sqrt.f64 (hypot.f64 re im)) (sqrt.f64 (hypot.f64 re im)) re))))
	42.3b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 (pow.f64 (cbrt.f64 (hypot.f64 re im)) 2) (+.f64 (cbrt.f64 (hypot.f64 re im)) (/.f64 re (pow.f64 (cbrt.f64 (hypot.f64 re im)) 2)))))))
	42.3b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 (*.f64 (pow.f64 (cbrt.f64 (hypot.f64 re im)) 2) (cbrt.f64 (hypot.f64 re im))) re))))
	54.1b	(.f64 1/2 (.f64 (sqrt.f64 (pow.f64 (exp.f64 (.f64 (log.f64 (/.f64 (pow.f64 (.f64 (+.f64 re (hypot.f64 re im)) 2) 2) (+.f64 (pow.f64 (.f64 (+.f64 re (hypot.f64 re im)) 2) 4/3) (+.f64 0 (.f64 (pow.f64 (.f64 (+.f64 re (hypot.f64 re im)) 2) 2/3) 0))))) 1/2)) 2)) (sqrt.f64 (cbrt.f64 (.f64 (+.f64 re (hypot.f64 re im)) 2)))))
	46.3b	(.f64 1/2 (.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (.f64 (+.f64 re (hypot.f64 re im)) 2)) 2)) (sqrt.f64 (.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (.f64 (+.f64 re (hypot.f64 re im)) 2)) 4))) (sqrt.f64 (cbrt.f64 (pow.f64 (.f64 (+.f64 re (hypot.f64 re im)) 2) 2/3)))))))
	41.6b	(.f64 1/2 (.f64 (sqrt.f64 (.f64 (pow.f64 (pow.f64 (.f64 (+.f64 re (hypot.f64 re im)) 2) 2/3) 2/3) (pow.f64 (cbrt.f64 (.f64 (+.f64 re (hypot.f64 re im)) 2)) 2/3))) (sqrt.f64 (exp.f64 (.f64 (log.f64 (pow.f64 (*.f64 (+.f64 re (hypot.f64 re im)) 2) 2/3)) 1/2)))))
	45.6b	(.f64 1/2 (.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (.f64 (-.f64 re (fma.f64 1/2 (/.f64 (.f64 re re) im) im)) 2)) 2)) (sqrt.f64 (cbrt.f64 (*.f64 (+.f64 re (hypot.f64 re im)) 2)))))
	44.0b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 (pow.f64 (cbrt.f64 re) 2) (+.f64 (cbrt.f64 re) (/.f64 (hypot.f64 re im) (pow.f64 (cbrt.f64 re) 2)))))))
	42.8b	(.f64 1/2 (sqrt.f64 (.f64 2 (fma.f64 (pow.f64 (cbrt.f64 (hypot.f64 re im)) 2) (cbrt.f64 (hypot.f64 re im)) re))))
	48.4b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 (-.f64 (exp.f64 (log1p.f64 (hypot.f64 re im))) 1) re))))
	45.7b	(.f64 1/2 (.f64 (sqrt.f64 (-.f64 (exp.f64 (log1p.f64 (pow.f64 (.f64 (+.f64 re (hypot.f64 re im)) 2) 2/3))) 1)) (sqrt.f64 (exp.f64 (.f64 (log.f64 (pow.f64 (*.f64 (+.f64 re (hypot.f64 re im)) 2) 2/3)) 1/2)))))
	42.2b	(.f64 1/2 (sqrt.f64 (.f64 2 (fma.f64 (pow.f64 (cbrt.f64 re) 2) (cbrt.f64 re) (hypot.f64 re im)))))
	43.8b	(.f64 1/2 (.f64 (sqrt.f64 (pow.f64 (exp.f64 (.f64 1/3 (-.f64 (log.f64 2) (log.f64 (/.f64 1 im))))) 2)) (sqrt.f64 (exp.f64 (.f64 (log.f64 (pow.f64 (*.f64 (+.f64 re (hypot.f64 re im)) 2) 2/3)) 1/2)))))
	42.6b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 re (+.f64 1 (/.f64 (hypot.f64 re im) re))))))
	41.7b	(.f64 1/2 (.f64 (sqrt.f64 (pow.f64 (pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (cbrt.f64 (.f64 (+.f64 re (hypot.f64 re im)) 2)))) 2)) (cbrt.f64 (log.f64 (cbrt.f64 (.f64 (+.f64 re (hypot.f64 re im)) 2))))) 2)) (sqrt.f64 (exp.f64 (.f64 (log.f64 (pow.f64 (.f64 (+.f64 re (hypot.f64 re im)) 2) 2/3)) 1/2)))))
	56.0b	(.f64 1/2 (sqrt.f64 (.f64 2 (+.f64 (/.f64 (pow.f64 (hypot.f64 re im) 3) (+.f64 (pow.f64 (hypot.f64 re im) 2) (+.f64 0 (*.f64 (hypot.f64 re im) 0)))) re))))
	41.8b	(.f64 1/2 (sqrt.f64 (.f64 2 (*.f64 (sqrt.f64 (hypot.f64 re im)) (+.f64 (sqrt.f64 (hypot.f64 re im)) (/.f64 re (sqrt.f64 (hypot.f64 re im))))))))
	54.0b	(.f64 1/2 (.f64 (sqrt.f64 (pow.f64 (exp.f64 (.f64 (log.f64 (/.f64 (pow.f64 (.f64 (+.f64 re (hypot.f64 re im)) 2) 2) (+.f64 (pow.f64 (.f64 (+.f64 re (hypot.f64 re im)) 2) 4/3) (-.f64 0 (.f64 (pow.f64 (.f64 (+.f64 re (hypot.f64 re im)) 2) 2/3) 0))))) 1/2)) 2)) (sqrt.f64 (exp.f64 (.f64 (log.f64 (pow.f64 (*.f64 (+.f64 re (hypot.f64 re im)) 2) 2/3)) 1/2)))))

Compiler

Compiled 31672 to 22582 computations (28.7% saved)

regimes4.2s (38.3%)

Accuracy

Total 4.9b remaining (39.7%)

Threshold costs 0b (0%)

Counts

355 → 2

Compiler

Compiled 74784 to 54493 computations (27.1% saved)

bsearch69.0ms (0.6%)

Steps

Iters	Range		Point
8	-1.0315144708934782e+64	-6.930294750975624e+60	-3.9425870866783413e+62

Compiler

Compiled 3 to 2 computations (33.3% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	47
1	23	47

end808.0ms (7.3%)

Remove: (sort re im)
Compiler: Compiled 1122 to 815 computations (27.4% saved)

Details

analyze443.0ms (4%)

sample1.8s (16.6%)

simplify35.0ms (0.3%)

prune4.0ms (0%)

localize9.0ms (0.1%)

series74.0ms (0.7%)

rewrite77.0ms (0.7%)

simplify76.0ms (0.7%)

prune207.0ms (1.9%)

localize11.0ms (0.1%)

series194.0ms (1.8%)

rewrite100.0ms (0.9%)

simplify95.0ms (0.9%)

prune750.0ms (6.8%)

localize17.0ms (0.2%)

series101.0ms (0.9%)

rewrite72.0ms (0.7%)

simplify64.0ms (0.6%)

prune637.0ms (5.8%)

localize14.0ms (0.1%)

series85.0ms (0.8%)

rewrite67.0ms (0.6%)

simplify117.0ms (1.1%)

prune830.0ms (7.5%)

regimes4.2s (38.3%)

bsearch69.0ms (0.6%)

simplify2.0ms (0%)

end808.0ms (7.3%)

Profiling