Details

analyze396.0ms (6.6%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	50%	0%	2
50%	50%	0%	3
62.5%	37.5%	0%	4
68.7%	31.2%	0%	5
71.8%	28.1%	0%	6
73.4%	26.5%	0%	7
74.2%	25.8%	0%	8
74.6%	25.4%	0%	9
74.8%	25.2%	0%	10
74.9%	25.1%	0%	11
74.9%	25%	0%	12
74.9%	25%	0%	13
75%	25%	0%	14

Compiler

Compiled 11 to 8 computations (27.3% saved)

sample3.4s (55.7%)

Results

1.5s	2607×	body	1024	valid
741.0ms	1272×	body	2048	valid
533.0ms	1266×	body	512	valid
280.0ms	2445×	body	128	valid
141.0ms	621×	body	256	valid
32.0ms	45×	body	4096	valid

Compiler

Compiled 32 to 23 computations (28.1% saved)

simplify77.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

377×	`fma-def_binary64`
372×	`log-div_binary64`
360×	`fma-neg_binary64`
336×	`rules-23-rev_binary64`
324×	`log-prod_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	12
1	16	9
2	27	9
3	48	9
4	112	9
5	296	9
6	1124	9
7	3392	9
8	4224	9
9	4984	9

prune3.0ms (0%)

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

47.5b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	47.5b	(log.f64 (+.f64 x (hypot.f64 1 x)))

Compiler

Compiled 30 to 21 computations (30% saved)

localize4.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	1.4b	(+.f64 x (hypot.f64 1 x))
✓	4.0b	(log.f64 (+.f64 x (hypot.f64 1 x)))

series7.0ms (0.1%)

Counts

2 → 24

Calls

2 calls:

3.0ms	(log.f64 (+.f64 x (hypot.f64 1 x)))
3.0ms	(+.f64 x (hypot.f64 1 x))

rewrite51.0ms (0.8%)

Algorithm

2×	batch-egg-rewrite

Rules

563×	`log1p-expm1-u_binary64`
563×	`expm1-log1p-u_binary64`
457×	`fma-neg_binary64`
364×	`prod-diff_binary64`
101×	`expm1-udef_binary64`

Counts

2 → 94

Calls

2 calls:

49.0ms	(+.f64 x (hypot.f64 1 x))
49.0ms	(log.f64 (+.f64 x (hypot.f64 1 x)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	16
1	135	16
2	1620	16
3	4948	16
0	0	0
1	0	0

simplify30.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

389×	`fma-neg_binary64`
321×	`rules-15-rev_binary64`
244×	`rules-20_binary64`
238×	`rules-11_binary64`
211×	`rules-12-rev_binary64`

Counts

118 → 137

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	84	411
1	255	403
2	1154	393
3	5012	393

prune78.0ms (1.3%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	133	4	137
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	134	4	138

Error

0.0b

Counts

138 → 4

Alt Table

Status	Error	Program
	47.6b	(log.f64 (pow.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x))) 2))
	46.6b	(log.f64 (-.f64 (/.f64 1/8 (pow.f64 x 3)) (/.f64 1/2 x)))
▶	30.0b	(-.f64 x (*.f64 1/6 (pow.f64 x 3)))
	48.6b	(exp.f64 (log.f64 (log.f64 (+.f64 x (hypot.f64 1 x)))))

Compiler

Compiled 1909 to 1420 computations (25.6% saved)

localize4.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 x (*.f64 1/6 (pow.f64 x 3)))
✓	0.1b	(*.f64 1/6 (pow.f64 x 3))

series7.0ms (0.1%)

Counts

2 → 3

Calls

2 calls:

4.0ms	(*.f64 1/6 (pow.f64 x 3))
3.0ms	(-.f64 x (*.f64 1/6 (pow.f64 x 3)))

rewrite64.0ms (1.1%)

Algorithm

2×	batch-egg-rewrite

Rules

714×	`log1p-expm1-u_binary64`
714×	`expm1-log1p-u_binary64`
665×	`prod-diff_binary64`
127×	`egg-rr`
72×	`add-sqr-sqrt_binary64`

Counts

2 → 127

Calls

2 calls:

61.0ms	(-.f64 x (*.f64 1/6 (pow.f64 x 3)))
61.0ms	(*.f64 1/6 (pow.f64 x 3))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	17
1	170	17
2	2062	17
3	5728	17
0	0	0
1	0	0

simplify65.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

1005×	`fma-neg_binary64`
549×	`cube-div_binary64`
403×	`rules-20_binary64`
342×	`rules-24-rev_binary64`
330×	`rules-5-rev_binary64`

Counts

130 → 129

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	15
1	10	15
2	19	15
3	26	15
4	49	15
5	97	15
6	220	15
7	600	15
8	1758	15
9	4125	15
10	4894	15

prune77.0ms (1.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	129	0	129
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	129	4	133

Error

0.0b

Counts

133 → 4

Alt Table

Status	Error	Program
	47.6b	(log.f64 (pow.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x))) 2))
▶	46.6b	(log.f64 (-.f64 (/.f64 1/8 (pow.f64 x 3)) (/.f64 1/2 x)))
✓	30.0b	(-.f64 x (*.f64 1/6 (pow.f64 x 3)))
	48.6b	(exp.f64 (log.f64 (log.f64 (+.f64 x (hypot.f64 1 x)))))

Compiler

Compiled 2744 to 1905 computations (30.6% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (/.f64 1/8 (pow.f64 x 3)) (/.f64 1/2 x))
✓	0.3b	(/.f64 1/8 (pow.f64 x 3))
✓	11.9b	(log.f64 (-.f64 (/.f64 1/8 (pow.f64 x 3)) (/.f64 1/2 x)))

series9.0ms (0.2%)

Counts

3 → 24

Calls

3 calls:

3.0ms	(log.f64 (-.f64 (/.f64 1/8 (pow.f64 x 3)) (/.f64 1/2 x)))
3.0ms	(-.f64 (/.f64 1/8 (pow.f64 x 3)) (/.f64 1/2 x))
3.0ms	(/.f64 1/8 (pow.f64 x 3))

rewrite79.0ms (1.3%)

Algorithm

2×	batch-egg-rewrite

Rules

680×	`fma-neg_binary64`
451×	`prod-diff_binary64`
432×	`fma-def_binary64`
195×	`egg-rr`
168×	`expm1-udef_binary64`

Counts

3 → 195

Calls

3 calls:

75.0ms	(-.f64 (/.f64 1/8 (pow.f64 x 3)) (/.f64 1/2 x))
75.0ms	(/.f64 1/8 (pow.f64 x 3))
75.0ms	(log.f64 (-.f64 (/.f64 1/8 (pow.f64 x 3)) (/.f64 1/2 x)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	35
1	234	35
2	2684	35
3	4866	35
0	0	0
1	0	0

simplify52.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

958×	`rules-14-rev_binary64`
403×	`rules-21_binary64`
218×	`rules-11_binary64`
196×	`fma-neg_binary64`
160×	`rules-13_binary64`

Counts

219 → 221

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	63	410
1	176	410
2	724	403
3	4185	402
4	6530	402

prune124.0ms (2.1%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	221	0	221
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	221	4	225

Error

0.0b

Counts

225 → 4

Alt Table

Status	Error	Program
▶	47.6b	(log.f64 (pow.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x))) 2))
✓	46.6b	(log.f64 (-.f64 (/.f64 1/8 (pow.f64 x 3)) (/.f64 1/2 x)))
✓	30.0b	(-.f64 x (*.f64 1/6 (pow.f64 x 3)))
	48.6b	(exp.f64 (log.f64 (log.f64 (+.f64 x (hypot.f64 1 x)))))

Compiler

Compiled 4676 to 3832 computations (18% saved)

localize6.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (+.f64 x (hypot.f64 1 x)))
✓	0.1b	(pow.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x))) 2)
	1.4b	(+.f64 x (hypot.f64 1 x))
✓	4.0b	(log.f64 (pow.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x))) 2))

series20.0ms (0.3%)

Counts

3 → 12

Calls

3 calls:

8.0ms	(log.f64 (pow.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x))) 2))
6.0ms	(pow.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x))) 2)
5.0ms	(sqrt.f64 (+.f64 x (hypot.f64 1 x)))

rewrite62.0ms (1%)

Algorithm

2×	batch-egg-rewrite

Rules

703×	`log1p-expm1-u_binary64`
703×	`expm1-log1p-u_binary64`
391×	`prod-diff_binary64`
133×	`egg-rr`
73×	`add-sqr-sqrt_binary64`

Counts

3 → 133

Calls

3 calls:

58.0ms	(sqrt.f64 (+.f64 x (hypot.f64 1 x)))
58.0ms	(pow.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x))) 2)
58.0ms	(log.f64 (pow.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x))) 2))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	25
1	188	25
2	2058	25
3	5222	25
0	0	0
1	0	0

simplify66.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

532×	`fma-neg_binary64`
452×	`rules-11_binary64`
356×	`rules-20_binary64`
339×	`fma-def_binary64`
242×	`rules-13_binary64`

Counts

145 → 152

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	40	133
1	102	125
2	345	122
3	1390	117
4	4821	117
5	4894	117
6	4958	117

prune149.0ms (2.5%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	236	1	237
Fresh	0	1	1
Picked	1	0	1
Done	0	2	2
Total	237	4	241

Error

0.0b

Counts

241 → 4

Alt Table

Status	Error	Program
	47.6b	(log.f64 (pow.f64 (*.f64 (cbrt.f64 (+.f64 x (hypot.f64 1 x))) (cbrt.f64 (sqrt.f64 (+.f64 x (hypot.f64 1 x))))) 2))
✓	46.6b	(log.f64 (-.f64 (/.f64 1/8 (pow.f64 x 3)) (/.f64 1/2 x)))
✓	30.0b	(-.f64 x (*.f64 1/6 (pow.f64 x 3)))
	48.6b	(exp.f64 (log.f64 (log.f64 (+.f64 x (hypot.f64 1 x)))))

Compiler

Compiled 3829 to 2920 computations (23.7% saved)

regimes1.1s (18.6%)

Accuracy

Total 0.1b remaining (69.3%)

Threshold costs 0.1b (69.3%)

Counts

109 → 3

Compiler

Compiled 3684 to 2965 computations (19.5% saved)

bsearch37.0ms (0.6%)

Steps

Iters	Range		Point
8	2.861332380623058e-6	0.021286450759173393	0.0010906364138287723
9	-4.83044265941669	-9.161204285302546e-6	-1.0730541910957112

Compiler

Compiled 2 to 1 computations (50% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	49
1	27	49
2	26	49

end75.0ms (1.2%)

Compiler: Compiled 114 to 88 computations (22.8% saved)

Details

analyze396.0ms (6.6%)

sample3.4s (55.7%)

simplify77.0ms (1.3%)

prune3.0ms (0%)

localize4.0ms (0.1%)

series7.0ms (0.1%)

rewrite51.0ms (0.8%)

simplify30.0ms (0.5%)

prune78.0ms (1.3%)

localize4.0ms (0.1%)

series7.0ms (0.1%)

rewrite64.0ms (1.1%)

simplify65.0ms (1.1%)

prune77.0ms (1.3%)

localize9.0ms (0.1%)

series9.0ms (0.2%)

rewrite79.0ms (1.3%)

simplify52.0ms (0.9%)

prune124.0ms (2.1%)

localize6.0ms (0.1%)

series20.0ms (0.3%)

rewrite62.0ms (1%)

simplify66.0ms (1.1%)

prune149.0ms (2.5%)

regimes1.1s (18.6%)

bsearch37.0ms (0.6%)

simplify2.0ms (0%)

end75.0ms (1.2%)

Profiling