Details

analyze1.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
100%	0%	0%	1

Compiler

Compiled 14 to 13 computations (7.1% saved)

sample2.2s (39%)

Results

1.1s	2167×	body	2048	valid
465.0ms	4313×	body	128	valid
397.0ms	1046×	body	1024	valid
144.0ms	502×	body	512	valid
42.0ms	228×	body	256	valid

Compiler

Compiled 41 to 38 computations (7.3% saved)

simplify64.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

894×	`fma-def_binary64`
376×	`rules-20_binary64`
351×	`rules-15_binary64`
321×	`rules-9-rev_binary64`
165×	`rules-6-rev_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	18
1	20	15
2	36	15
3	62	15
4	144	15
5	305	15
6	1364	15
7	3354	15
8	4895	15
9	4909	15

prune3.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

13.2b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	13.2b	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))

Compiler

Compiled 45 to 41 computations (8.9% saved)

localize7.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(hypot.f64 1 x)
✓	0.0b	(+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))
✓	0.0b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
✓	1.2b	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))

series15.0ms (0.3%)

Counts

4 → 48

Calls

4 calls:

5.0ms	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
4.0ms	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
3.0ms	(+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))
3.0ms	(hypot.f64 1 x)

rewrite79.0ms (1.4%)

Algorithm

2×	batch-egg-rewrite

Rules

891×	`log1p-expm1-u_binary64`
891×	`expm1-log1p-u_binary64`
378×	`prod-diff_binary64`
143×	`egg-rr`
91×	`add-sqr-sqrt_binary64`

Counts

4 → 143

Calls

4 calls:

76.0ms	(hypot.f64 1 x)
76.0ms	(+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))
76.0ms	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
76.0ms	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	41
1	215	41
2	2549	41
3	6449	41
0	0	0
1	0	0

simplify49.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

680×	`fma-neg_binary64`
607×	`rules-15-rev_binary64`
427×	`rules-20_binary64`
425×	`rules-14-rev_binary64`
294×	`fma-def_binary64`

Counts

191 → 224

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	122	901
1	428	880
2	2030	860
3	5594	860

prune185.0ms (3.3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	221	3	224
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	222	3	225

Error

0.0b

Counts

225 → 3

Alt Table

Status	Error	Program
	32.1b	(-.f64 (fma.f64 1/8 (.f64 x x) (.f64 69/1024 (pow.f64 x 6))) (*.f64 11/128 (pow.f64 x 4)))
	13.2b	(expm1.f64 (log1p.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))
▶	12.7b	(/.f64 (-.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 3/2)) (+.f64 1 (+.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))

Compiler

Compiled 4159 to 3681 computations (11.5% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
✓	0.0b	(/.f64 (-.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 3/2)) (+.f64 1 (+.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))
✓	0.0b	(pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 3/2)
✓	0.7b	(-.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 3/2))

series114.0ms (2%)

Counts

4 → 48

Calls

4 calls:

99.0ms	(/.f64 (-.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 3/2)) (+.f64 1 (+.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))
6.0ms	(+.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
5.0ms	(-.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 3/2))
3.0ms	(pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 3/2)

rewrite96.0ms (1.7%)

Algorithm

2×	batch-egg-rewrite

Rules

249×	`expm1-udef_binary64`
249×	`log1p-udef_binary64`
150×	`egg-rr`
146×	`log1p-expm1-u_binary64`
146×	`expm1-log1p-u_binary64`

Counts

4 → 150

Calls

4 calls:

91.0ms	(+.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
91.0ms	(/.f64 (-.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 3/2)) (+.f64 1 (+.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))
91.0ms	(pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 3/2)
91.0ms	(-.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 3/2))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	98
1	347	95
2	4132	95
3	4864	95
0	0	0
1	0	0

simplify93.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

995×	`fma-def_binary64`
848×	`rules-14-rev_binary64`
747×	`rules-21_binary64`
359×	`rules-20_binary64`
148×	`rules-2-rev_binary64`

Counts

198 → 233

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	585	5460
1	1984	4852
2	6086	4852

prune451.0ms (8%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	232	1	233
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	232	4	236

Error

Counts

236 → 4

Alt Table

Status	Error	Program
	31.7b	(/.f64 (*.f64 3/8 (pow.f64 x 2)) (+.f64 1 (+.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))
	32.1b	(-.f64 (fma.f64 1/8 (.f64 x x) (.f64 69/1024 (pow.f64 x 6))) (*.f64 11/128 (pow.f64 x 4)))
▶	13.2b	(expm1.f64 (log1p.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))
✓	12.7b	(/.f64 (-.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 3/2)) (+.f64 1 (+.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))

Compiler

Compiled 14266 to 12979 computations (9% saved)

localize14.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(log1p.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
✓	0.0b	(expm1.f64 (log1p.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))
	0.0b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
	1.2b	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))

series16.0ms (0.3%)

Counts

2 → 24

Calls

2 calls:

11.0ms	(log1p.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
5.0ms	(expm1.f64 (log1p.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))

rewrite104.0ms (1.8%)

Algorithm

2×	batch-egg-rewrite

Rules

794×	`fma-neg_binary64`
466×	`prod-diff_binary64`
175×	`expm1-udef_binary64`
175×	`log1p-udef_binary64`
99×	`add-sqr-sqrt_binary64`

Counts

2 → 72

Calls

2 calls:

102.0ms	(log1p.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
102.0ms	(expm1.f64 (log1p.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	32
1	237	32
2	2801	32
3	4897	32
4	4929	32
0	0	0
1	0	0

simplify51.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

754×	`rules-15-rev_binary64`
602×	`fma-neg_binary64`
544×	`rules-20_binary64`
451×	`fma-def_binary64`
349×	`rules-21_binary64`

Counts

96 → 112

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	130	992
1	454	924
2	2324	904
3	5929	904

prune188.0ms (3.3%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	218	0	218
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	218	4	222

Error

Counts

222 → 4

Alt Table

Status	Error	Program
▶	31.7b	(/.f64 (*.f64 3/8 (pow.f64 x 2)) (+.f64 1 (+.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))
	32.1b	(-.f64 (fma.f64 1/8 (.f64 x x) (.f64 69/1024 (pow.f64 x 6))) (*.f64 11/128 (pow.f64 x 4)))
✓	13.2b	(expm1.f64 (log1p.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))
✓	12.7b	(/.f64 (-.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 3/2)) (+.f64 1 (+.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))

Compiler

Compiled 5165 to 4665 computations (9.7% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
	0.0b	(+.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
✓	0.1b	(*.f64 3/8 (pow.f64 x 2))
✓	0.1b	(/.f64 (*.f64 3/8 (pow.f64 x 2)) (+.f64 1 (+.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))

series66.0ms (1.2%)

Counts

2 → 12

Calls

2 calls:

63.0ms	(/.f64 (*.f64 3/8 (pow.f64 x 2)) (+.f64 1 (+.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))
3.0ms	(*.f64 3/8 (pow.f64 x 2))

rewrite86.0ms (1.5%)

Algorithm

2×	batch-egg-rewrite

Rules

264×	`expm1-udef_binary64`
264×	`log1p-udef_binary64`
151×	`add-sqr-sqrt_binary64`
150×	`log1p-expm1-u_binary64`
150×	`expm1-log1p-u_binary64`

Counts

2 → 60

Calls

2 calls:

85.0ms	(*.f64 3/8 (pow.f64 x 2))
85.0ms	(/.f64 (*.f64 3/8 (pow.f64 x 2)) (+.f64 1 (+.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	43
1	368	40
2	4364	40
3	4960	40
0	0	0
1	0	0

simplify62.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

439×	`rules-15-rev_binary64`
359×	`fma-neg_binary64`
332×	`fma-def_binary64`
300×	`rules-13_binary64`
278×	`rules-14-rev_binary64`

Counts

72 → 83

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	229	1646
1	699	1219
2	4129	1219
3	5708	1219

prune252.0ms (4.5%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	214	0	214
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	214	4	218

Error

Counts

218 → 4

Alt Table

Status	Error	Program
✓	31.7b	(/.f64 (*.f64 3/8 (pow.f64 x 2)) (+.f64 1 (+.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))
	32.1b	(-.f64 (fma.f64 1/8 (.f64 x x) (.f64 69/1024 (pow.f64 x 6))) (*.f64 11/128 (pow.f64 x 4)))
✓	13.2b	(expm1.f64 (log1p.f64 (-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))
✓	12.7b	(/.f64 (-.f64 1 (pow.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) 3/2)) (+.f64 1 (+.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))

Compiler

Compiled 8207 to 7214 computations (12.1% saved)

regimes1.3s (23.1%)

Accuracy

Total 0.0b remaining (56.6%)

Threshold costs 0.0b (56.6%)

Counts

174 → 2

Compiler

Compiled 21992 to 19842 computations (9.8% saved)

bsearch5.0ms (0.1%)

Compiler: Compiled 4 to 3 computations (25% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	76
1	33	76
2	32	76

end111.0ms (2%)

Compiler: Compiled 190 to 163 computations (14.2% saved)

Details

analyze1.0ms (0%)

sample2.2s (39%)

simplify64.0ms (1.1%)

prune3.0ms (0.1%)

localize7.0ms (0.1%)

series15.0ms (0.3%)

rewrite79.0ms (1.4%)

simplify49.0ms (0.9%)

prune185.0ms (3.3%)

localize11.0ms (0.2%)

series114.0ms (2%)

rewrite96.0ms (1.7%)

simplify93.0ms (1.6%)

prune451.0ms (8%)

localize14.0ms (0.3%)

series16.0ms (0.3%)

rewrite104.0ms (1.8%)

simplify51.0ms (0.9%)

prune188.0ms (3.3%)

localize11.0ms (0.2%)

series66.0ms (1.2%)

rewrite86.0ms (1.5%)

simplify62.0ms (1.1%)

prune252.0ms (4.5%)

regimes1.3s (23.1%)

bsearch5.0ms (0.1%)

simplify3.0ms (0.1%)

end111.0ms (2%)

Profiling