Details

analyze5.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	50%	50%	3
25%	25%	50%	4
37.5%	12.5%	50%	5
43.7%	6.2%	50%	6
46.9%	3.1%	50%	7
48.4%	1.6%	50%	8
49.2%	0.8%	50%	9
49.6%	0.4%	50%	10
49.8%	0.2%	50%	11
49.9%	0.1%	50%	12
49.9%	0%	50%	13
49.9%	0%	50%	14

Compiler

Compiled 10 to 8 computations (20% saved)

sample3.8s (77.3%)

Results

2.3s	4114×	body	1024	valid
739.0ms	2086×	body	512	valid
360.0ms	407×	body	2048	valid
250.0ms	1065×	body	256	valid
73.0ms	584×	body	128	valid

Compiler

Compiled 29 to 23 computations (20.7% saved)

simplify9.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

1×	`rules-21_binary64`
1×	`rules-53-rev_binary64`
1×	`1-exp_binary64`
1×	`log-div_binary64`
1×	`log1p-def_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	12
1	13	11
2	16	11
3	15	11

prune4.0ms (0.1%)

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

50.5b

Counts

3 → 2

Alt Table

Status	Error	Program
	58.7b	(log.f64 (/.f64 (-.f64 1 eps) (+.f64 1 eps)))
▶	50.5b	(-.f64 (log.f64 (-.f64 1 eps)) (log1p.f64 eps))

Compiler

Compiled 50 to 38 computations (24% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (log.f64 (-.f64 1 eps)) (log1p.f64 eps))
✓	4.7b	(log.f64 (-.f64 1 eps))

series6.0ms (0.1%)

Counts

2 → 24

Calls

2 calls:

3.0ms	(-.f64 (log.f64 (-.f64 1 eps)) (log1p.f64 eps))
3.0ms	(log.f64 (-.f64 1 eps))

rewrite50.0ms (1%)

Algorithm

2×	batch-egg-rewrite

Rules

691×	`expm1-log1p-u_binary64`
690×	`log1p-expm1-u_binary64`
475×	`prod-diff_binary64`
77×	`egg-rr`
69×	`add-sqr-sqrt_binary64`

Counts

2 → 77

Calls

2 calls:

49.0ms	(-.f64 (log.f64 (-.f64 1 eps)) (log1p.f64 eps))
49.0ms	(log.f64 (-.f64 1 eps))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	17
1	160	17
2	1954	17
3	5326	17
0	0	0
1	0	0

simplify49.0ms (1%)

Algorithm

1×	egg-herbie

Rules

465×	`fma-def_binary64`
433×	`rules-13_binary64`
405×	`fma-neg_binary64`
365×	`rules-14-rev_binary64`
253×	`rules-21_binary64`

Counts

101 → 121

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	90	411
1	264	405
2	1034	395
3	4940	395
4	5345	395

prune59.0ms (1.2%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	120	1	121
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	121	2	123

Error

0.0b

Counts

123 → 2

Alt Table

Status	Error	Program
	58.7b	(log.f64 (/.f64 (-.f64 1 eps) (+.f64 1 eps)))
▶	0.1b	(neg.f64 (fma.f64 2/7 (pow.f64 eps 7) (fma.f64 eps 2 (fma.f64 (pow.f64 eps 3) 2/3 (*.f64 2/5 (pow.f64 eps 5))))))

Compiler

Compiled 1868 to 1259 computations (32.6% saved)

localize11.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 2/7 (pow.f64 eps 7) (fma.f64 eps 2 (fma.f64 (pow.f64 eps 3) 2/3 (*.f64 2/5 (pow.f64 eps 5)))))
✓	0.1b	(*.f64 2/5 (pow.f64 eps 5))
✓	0.1b	(fma.f64 (pow.f64 eps 3) 2/3 (*.f64 2/5 (pow.f64 eps 5)))

series12.0ms (0.2%)

Counts

3 → 24

Calls

3 calls:

4.0ms	(fma.f64 2/7 (pow.f64 eps 7) (fma.f64 eps 2 (fma.f64 (pow.f64 eps 3) 2/3 (*.f64 2/5 (pow.f64 eps 5)))))
4.0ms	(fma.f64 (pow.f64 eps 3) 2/3 (*.f64 2/5 (pow.f64 eps 5)))
3.0ms	(*.f64 2/5 (pow.f64 eps 5))

rewrite72.0ms (1.5%)

Algorithm

2×	batch-egg-rewrite

Rules

267×	`expm1-udef_binary64`
267×	`log1p-udef_binary64`
194×	`prod-diff_binary64`
153×	`add-sqr-sqrt_binary64`
149×	`log1p-expm1-u_binary64`

Counts

3 → 96

Calls

3 calls:

70.0ms	(fma.f64 2/7 (pow.f64 eps 7) (fma.f64 eps 2 (fma.f64 (pow.f64 eps 3) 2/3 (*.f64 2/5 (pow.f64 eps 5)))))
70.0ms	(*.f64 2/5 (pow.f64 eps 5))
70.0ms	(fma.f64 (pow.f64 eps 3) 2/3 (*.f64 2/5 (pow.f64 eps 5)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	46
1	379	46
2	4018	46
3	4921	46
0	0	0
1	0	0

simplify64.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

899×	`fma-def_binary64`
634×	`rules-13_binary64`
626×	`rules-14_binary64`
618×	`rules-5_binary64`
295×	`rules-20_binary64`

Counts

120 → 114

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	339
1	63	339
2	239	339
3	991	339
4	4437	339
5	4225	339
6	5257	339

prune98.0ms (2%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	114	0	114
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	114	2	116

Error

0.0b

Counts

116 → 2

Alt Table

Status	Error	Program
▶	58.7b	(log.f64 (/.f64 (-.f64 1 eps) (+.f64 1 eps)))
✓	0.1b	(neg.f64 (fma.f64 2/7 (pow.f64 eps 7) (fma.f64 eps 2 (fma.f64 (pow.f64 eps 3) 2/3 (*.f64 2/5 (pow.f64 eps 5))))))

Compiler

Compiled 2837 to 2313 computations (18.5% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 1 eps) (+.f64 1 eps))
✓	4.7b	(log.f64 (/.f64 (-.f64 1 eps) (+.f64 1 eps)))

series5.0ms (0.1%)

Counts

2 → 24

Calls

2 calls:

3.0ms	(log.f64 (/.f64 (-.f64 1 eps) (+.f64 1 eps)))
2.0ms	(/.f64 (-.f64 1 eps) (+.f64 1 eps))

rewrite53.0ms (1.1%)

Algorithm

2×	batch-egg-rewrite

Rules

677×	`log1p-expm1-u_binary64`
677×	`expm1-log1p-u_binary64`
310×	`prod-diff_binary64`
78×	`egg-rr`
69×	`add-sqr-sqrt_binary64`

Counts

2 → 78

Calls

2 calls:

51.0ms	(/.f64 (-.f64 1 eps) (+.f64 1 eps))
51.0ms	(log.f64 (/.f64 (-.f64 1 eps) (+.f64 1 eps)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	22
1	160	21
2	1938	21
3	4975	21
0	0	0
1	0	0

simplify44.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

794×	`fma-neg_binary64`
625×	`rules-15-rev_binary64`
364×	`rules-21_binary64`
186×	`fma-def_binary64`
184×	`rules-4_binary64`

Counts

102 → 106

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	56	322
1	175	318
2	725	312
3	3179	304
4	5426	304

prune46.0ms (0.9%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	105	1	106
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	105	3	108

Error

0.0b

Counts

108 → 3

Alt Table

Status	Error	Program
✓	58.7b	(log.f64 (/.f64 (-.f64 1 eps) (+.f64 1 eps)))
▶	58.8b	(+.f64 (log.f64 (pow.f64 (cbrt.f64 (/.f64 (-.f64 1 eps) (+.f64 1 eps))) 2)) (log.f64 (cbrt.f64 (/.f64 (-.f64 1 eps) (+.f64 1 eps)))))
✓	0.1b	(neg.f64 (fma.f64 2/7 (pow.f64 eps 7) (fma.f64 eps 2 (fma.f64 (pow.f64 eps 3) 2/3 (*.f64 2/5 (pow.f64 eps 5))))))

Compiler

Compiled 1686 to 1125 computations (33.3% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (log.f64 (pow.f64 (cbrt.f64 (/.f64 (-.f64 1 eps) (+.f64 1 eps))) 2)) (log.f64 (cbrt.f64 (/.f64 (-.f64 1 eps) (+.f64 1 eps)))))
✓	0.0b	(cbrt.f64 (/.f64 (-.f64 1 eps) (+.f64 1 eps)))
✓	4.7b	(log.f64 (pow.f64 (cbrt.f64 (/.f64 (-.f64 1 eps) (+.f64 1 eps))) 2))
✓	4.7b	(log.f64 (cbrt.f64 (/.f64 (-.f64 1 eps) (+.f64 1 eps))))

series40.0ms (0.8%)

Counts

4 → 48

Calls

4 calls:

16.0ms	(+.f64 (log.f64 (pow.f64 (cbrt.f64 (/.f64 (-.f64 1 eps) (+.f64 1 eps))) 2)) (log.f64 (cbrt.f64 (/.f64 (-.f64 1 eps) (+.f64 1 eps)))))
11.0ms	(log.f64 (cbrt.f64 (/.f64 (-.f64 1 eps) (+.f64 1 eps))))
9.0ms	(log.f64 (pow.f64 (cbrt.f64 (/.f64 (-.f64 1 eps) (+.f64 1 eps))) 2))
4.0ms	(cbrt.f64 (/.f64 (-.f64 1 eps) (+.f64 1 eps)))

rewrite83.0ms (1.7%)

Algorithm

2×	batch-egg-rewrite

Rules

697×	`prod-diff_binary64`
193×	`expm1-udef_binary64`
193×	`log1p-udef_binary64`
148×	`egg-rr`
113×	`add-sqr-sqrt_binary64`

Counts

4 → 148

Calls

4 calls:

80.0ms	(+.f64 (log.f64 (pow.f64 (cbrt.f64 (/.f64 (-.f64 1 eps) (+.f64 1 eps))) 2)) (log.f64 (cbrt.f64 (/.f64 (-.f64 1 eps) (+.f64 1 eps)))))
80.0ms	(cbrt.f64 (/.f64 (-.f64 1 eps) (+.f64 1 eps)))
80.0ms	(log.f64 (pow.f64 (cbrt.f64 (/.f64 (-.f64 1 eps) (+.f64 1 eps))) 2))
80.0ms	(log.f64 (cbrt.f64 (/.f64 (-.f64 1 eps) (+.f64 1 eps))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	55
1	276	52
2	3204	52
3	5076	52
0	0	0
1	0	0

simplify59.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

916×	`fma-neg_binary64`
537×	`fma-def_binary64`
447×	`rules-13_binary64`
362×	`rules-20_binary64`
264×	`rules-14-rev_binary64`

Counts

196 → 209

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	117	803
1	389	755
2	1580	719
3	4909	719
4	5600	719

prune164.0ms (3.3%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	259	1	260
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	259	4	263

Error

0.0b

Counts

263 → 4

Alt Table

Status	Error	Program
✓	58.7b	(log.f64 (/.f64 (-.f64 1 eps) (+.f64 1 eps)))
	58.7b	(+.f64 (-.f64 (exp.f64 (log1p.f64 (log.f64 (pow.f64 (/.f64 (-.f64 1 eps) (+.f64 1 eps)) 2/3)))) 1) (log.f64 (cbrt.f64 (/.f64 (-.f64 1 eps) (+.f64 1 eps)))))
✓	58.8b	(+.f64 (log.f64 (pow.f64 (cbrt.f64 (/.f64 (-.f64 1 eps) (+.f64 1 eps))) 2)) (log.f64 (cbrt.f64 (/.f64 (-.f64 1 eps) (+.f64 1 eps)))))
✓	0.1b	(neg.f64 (fma.f64 2/7 (pow.f64 eps 7) (fma.f64 eps 2 (fma.f64 (pow.f64 eps 3) 2/3 (*.f64 2/5 (pow.f64 eps 5))))))

Compiler

Compiled 6675 to 5476 computations (18% saved)

regimes63.0ms (1.3%)

Accuracy

Total 0.2b remaining (93.9%)

Threshold costs 0.2b (93.9%)

Counts

26 → 1

Compiler

Compiled 1160 to 908 computations (21.7% saved)

simplify1.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	27
1	17	27

end96.0ms (2%)

Compiler: Compiled 116 to 94 computations (19% saved)

Details

analyze5.0ms (0.1%)

sample3.8s (77.3%)

simplify9.0ms (0.2%)

prune4.0ms (0.1%)

localize5.0ms (0.1%)

series6.0ms (0.1%)

rewrite50.0ms (1%)

simplify49.0ms (1%)

prune59.0ms (1.2%)

localize11.0ms (0.2%)

series12.0ms (0.2%)

rewrite72.0ms (1.5%)

simplify64.0ms (1.3%)

prune98.0ms (2%)

localize5.0ms (0.1%)

series5.0ms (0.1%)

rewrite53.0ms (1.1%)

simplify44.0ms (0.9%)

prune46.0ms (0.9%)

localize9.0ms (0.2%)

series40.0ms (0.8%)

rewrite83.0ms (1.7%)

simplify59.0ms (1.2%)

prune164.0ms (3.3%)

regimes63.0ms (1.3%)

simplify1.0ms (0%)

end96.0ms (2%)

Profiling