Details

analyze5.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
50%	25%	25%	4
50%	12.5%	37.5%	5
50%	6.2%	43.8%	6
50%	3.1%	46.9%	7
50%	1.6%	48.5%	8
50%	0.8%	49.2%	9
50.4%	0.4%	49.2%	10
50.4%	0.2%	49.4%	11
50.4%	0.1%	49.5%	12
50.4%	0%	49.6%	13
50.4%	0%	49.6%	14

Compiler

Compiled 10 to 8 computations (20% saved)

sample163.0ms (3.6%)

Algorithm

1×

intervals

Results

64.0ms	125×	body	2048	valid
20.0ms	70×	body	1024	valid
4.0ms	30×	body	512	valid
2.0ms	24×	body	256	valid
0.0ms	7×	body	128	valid

Compiler

Compiled 20 to 16 computations (20% saved)

simplify58.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

819×	`div-sub_binary64`
801×	`associate-/l*_binary64`
624×	`fma-def_binary64`
581×	`fma-neg_binary64`
548×	`unswap-sqr_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	13
1	20	13
2	35	13
3	57	13
4	112	13
5	223	13
6	481	13
7	890	13
8	1570	13
9	4778	13
10	5815	13

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

32.1b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	32.1b	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))

Compiler

Compiled 27 to 21 computations (22.2% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (exp.f64 x) 2)
✓	4.2b	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))

series5.0ms (0.1%)

Counts

2 → 16

Calls

2 calls:

3.0ms	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))
2.0ms	(-.f64 (exp.f64 x) 2)

rewrite21.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

27×	`*-un-lft-identity_binary64`
22×	`add-sqr-sqrt_binary64`
18×	`prod-diff_binary64`
18×	`add-cube-cbrt_binary64`
13×	`associate-+l+_binary64`

Counts

2 → 69

Calls

2 calls:

8.0ms	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))
4.0ms	(-.f64 (exp.f64 x) 2)

simplify79.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

650×	`fma-neg_binary64`
326×	`fma-def_binary64`
296×	`distribute-rgt-in_binary64`
282×	`distribute-lft-in_binary64`
268×	`distribute-rgt-out_binary64`

Counts

85 → 114

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	145	1174
1	295	959
2	717	942
3	2801	932
4	4435	932
5	4838	932

prune70.0ms (1.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	111	3	114
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	111	4	115

Error

Counts

115 → 4

Alt Table

Status	Error	Program
✓	32.1b	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))
▶	0.3b	(fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (*.f64 1/20160 (pow.f64 x 8)))))
	0.5b	(fma.f64 x x (*.f64 1/12 (pow.f64 x 4)))
	32.1b	(expm1.f64 (log1p.f64 (+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))))

Compiler

Compiled 2103 to 1202 computations (42.8% saved)

localize10.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (*.f64 1/20160 (pow.f64 x 8))))
✓	0.0b	(fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (*.f64 1/20160 (pow.f64 x 8)))))
✓	0.0b	(*.f64 1/20160 (pow.f64 x 8))

series16.0ms (0.4%)

Counts

3 → 24

Calls

3 calls:

8.0ms

(*.f64 1/20160 (pow.f64 x 8))

5.0ms

(fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (*.f64 1/20160 (pow.f64 x 8))))

4.0ms

(fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (*.f64 1/20160 (pow.f64 x 8)))))

rewrite6.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-sqr-sqrt_binary64`
8×	`add-exp-log_binary64`
7×	`associate-r_binary64`
6×	`*-un-lft-identity_binary64`
6×	`add-cube-cbrt_binary64`

Counts

3 → 47

Calls

3 calls:

4.0ms

(*.f64 1/20160 (pow.f64 x 8))

0.0ms

(fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (*.f64 1/20160 (pow.f64 x 8)))))

0.0ms

(fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (*.f64 1/20160 (pow.f64 x 8))))

simplify52.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

798×	`fma-def_binary64`
562×	`associate-+l+_binary64`
546×	`associate-+r+_binary64`
247×	`associate-l_binary64`
214×	`associate-r_binary64`

Counts

71 → 71

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	91	1228
1	162	1128
2	390	1110
3	1598	1110
4	5154	1110

prune71.0ms (1.6%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	71	0	71
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	71	4	75

Error

Counts

75 → 4

Alt Table

Status	Error	Program
✓	32.1b	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))
✓	0.3b	(fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (*.f64 1/20160 (pow.f64 x 8)))))
▶	0.5b	(fma.f64 x x (*.f64 1/12 (pow.f64 x 4)))
	32.1b	(expm1.f64 (log1p.f64 (+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))))

Compiler

Compiled 1657 to 1247 computations (24.7% saved)

localize4.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x x (*.f64 1/12 (pow.f64 x 4)))
✓	0.1b	(*.f64 1/12 (pow.f64 x 4))

series7.0ms (0.1%)

Counts

2 → 12

Calls

2 calls:

4.0ms	(fma.f64 x x (*.f64 1/12 (pow.f64 x 4)))
3.0ms	(*.f64 1/12 (pow.f64 x 4))

rewrite5.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-sqr-sqrt_binary64`
7×	`associate-r_binary64`
7×	`add-exp-log_binary64`
5×	`*-un-lft-identity_binary64`
5×	`add-cube-cbrt_binary64`

Counts

2 → 37

Calls

2 calls:

4.0ms	(*.f64 1/12 (pow.f64 x 4))
0.0ms	(fma.f64 x x (*.f64 1/12 (pow.f64 x 4)))

simplify79.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

703×	`fma-def_binary64`
562×	`unswap-sqr_binary64`
352×	`*-commutative_binary64`
333×	`distribute-rgt-out_binary64`
291×	`distribute-lft-out_binary64`

Counts

49 → 49

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	66	570
1	110	535
2	240	517
3	668	517
4	1295	511
5	3475	506
6	4962	506
7	4950	506

prune40.0ms (0.9%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	49	0	49
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	49	4	53

Error

Counts

53 → 4

Alt Table

Status	Error	Program
✓	32.1b	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))
✓	0.3b	(fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (*.f64 1/20160 (pow.f64 x 8)))))
✓	0.5b	(fma.f64 x x (*.f64 1/12 (pow.f64 x 4)))
▶	32.1b	(expm1.f64 (log1p.f64 (+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))))

Compiler

Compiled 705 to 494 computations (29.9% saved)

localize7.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(log1p.f64 (+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x))))
✓	0.0b	(expm1.f64 (log1p.f64 (+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))))
	0.0b	(-.f64 (exp.f64 x) 2)
	4.2b	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))

series287.0ms (6.3%)

Counts

2 → 24

Calls

2 calls:

284.0ms	(log1p.f64 (+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x))))
3.0ms	(expm1.f64 (log1p.f64 (+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))))

rewrite2.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`expm1-log1p-u_binary64`
2×	`*-un-lft-identity_binary64`
2×	`add-sqr-sqrt_binary64`
2×	`add-cube-cbrt_binary64`
2×	`add-cbrt-cube_binary64`

Counts

2 → 22

Calls

2 calls:

0.0ms	(log1p.f64 (+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x))))
0.0ms	(expm1.f64 (log1p.f64 (+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))))

simplify58.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

877×	`distribute-rgt-in_binary64`
831×	`distribute-lft-in_binary64`
815×	`fma-def_binary64`
496×	`fma-neg_binary64`
246×	`cancel-sign-sub-inv_binary64`

Counts

46 → 55

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	70	760
1	145	671
2	369	636
3	1201	624
4	4661	624
5	4946	624

prune104.0ms (2.3%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	169	0	169
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	169	4	173

Error

Counts

173 → 4

Alt Table

Status	Error	Program
✓	32.1b	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))
✓	0.3b	(fma.f64 1/12 (pow.f64 x 4) (fma.f64 1/360 (pow.f64 x 6) (fma.f64 x x (*.f64 1/20160 (pow.f64 x 8)))))
✓	0.5b	(fma.f64 x x (*.f64 1/12 (pow.f64 x 4)))
✓	32.1b	(expm1.f64 (log1p.f64 (+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))))

Compiler

Compiled 3072 to 1819 computations (40.8% saved)

regimes40.0ms (0.9%)

Accuracy

Total 0.5b remaining (97.8%)

Threshold costs 0.5b (97.8%)

Counts

23 → 1

Compiler

Compiled 538 to 418 computations (22.3% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

3×	`+-commutative_binary64`
3×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	31
1	25	31
2	25	31

end1.0ms (0%)

Compiler: Compiled 22 to 18 computations (18.2% saved)

sample3.4s (73.7%)

Algorithm

1×

intervals

Results

2.4s	4214×	body	2048	valid
506.0ms	1934×	body	1024	valid
137.0ms	996×	body	512	valid
42.0ms	507×	body	256	valid
15.0ms	349×	body	128	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 81 to 63 computations (22.2% saved)

Details

analyze5.0ms (0.1%)

sample163.0ms (3.6%)

simplify58.0ms (1.3%)

prune2.0ms (0%)

localize6.0ms (0.1%)

series5.0ms (0.1%)

rewrite21.0ms (0.5%)

simplify79.0ms (1.7%)

prune70.0ms (1.5%)

localize10.0ms (0.2%)

series16.0ms (0.4%)

rewrite6.0ms (0.1%)

simplify52.0ms (1.1%)

prune71.0ms (1.6%)

localize4.0ms (0.1%)

series7.0ms (0.1%)

rewrite5.0ms (0.1%)

simplify79.0ms (1.7%)

prune40.0ms (0.9%)

localize7.0ms (0.2%)

series287.0ms (6.3%)

rewrite2.0ms (0%)

simplify58.0ms (1.3%)

prune104.0ms (2.3%)

regimes40.0ms (0.9%)

simplify2.0ms (0%)

end1.0ms (0%)

sample3.4s (73.7%)

Profiling