Details

analyze55.0ms (2.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	18.7%	81.3%	0
0%	18.7%	81.3%	1
0%	18.7%	81.3%	2
0%	18.7%	81.3%	3
0%	18.7%	81.3%	4
4.7%	14%	81.3%	5
5.3%	13.5%	81.3%	6
18.1%	0.6%	81.3%	7
18.1%	0.6%	81.3%	8
18.6%	0.1%	81.3%	9
18.6%	0.1%	81.3%	10
18.7%	0%	81.3%	11
18.7%	0%	81.3%	12
18.7%	0%	81.3%	13
18.7%	0%	81.3%	14

Compiler

Compiled 28 to 17 computations (39.3% saved)

sample279.0ms (11.4%)

Algorithm

1×

intervals

Results

12.0ms	256×	body	128	valid
5.0ms	256×	pre	128	true

Compiler

Compiled 47 to 28 computations (40.4% saved)

simplify82.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

917×	`times-frac_binary64`
816×	`unsub-neg_binary64`
772×	`fma-def_binary64`
484×	`fma-neg_binary64`
376×	`sub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	20
1	24	20
2	55	20
3	112	20
4	271	20
5	657	20
6	1234	20
7	2620	20
8	3288	20
9	4652	20
10	5075	20

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

20.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	20.1b	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (fma.f64 x x (.f64 y y)))

Compiler

Compiled 63 to 27 computations (57.1% saved)

localize8.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x x (*.f64 y y))
✓	19.8b	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (fma.f64 x x (.f64 y y)))

series25.0ms (1%)

Counts

2 → 48

Calls

2 calls:

19.0ms	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (fma.f64 x x (.f64 y y)))
6.0ms	(fma.f64 x x (*.f64 y y))

rewrite11.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`associate-/l/_binary64`
7×	`add-cbrt-cube_binary64`
7×	`add-exp-log_binary64`
4×	`frac-times_binary64`
4×	`*-un-lft-identity_binary64`

Counts

2 → 41

Calls

2 calls:

8.0ms	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (fma.f64 x x (.f64 y y)))
0.0ms	(fma.f64 x x (*.f64 y y))

simplify61.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

843×	`distribute-rgt-in_binary64`
815×	`distribute-lft-in_binary64`
413×	`times-frac_binary64`
413×	`fma-def_binary64`
73×	`cancel-sign-sub-inv_binary64`

Counts

89 → 76

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	108	1667
1	332	1473
2	1320	1435
3	5254	1435

prune39.0ms (1.6%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	73	3	76
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	74	3	77

Error

0.0b

Counts

77 → 3

Alt Table

Status	Error	Program
▶	0.0b	(*.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (/.f64 (+.f64 x y) (hypot.f64 x y)))
	20.1b	(log1p.f64 (expm1.f64 (/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (fma.f64 x x (.f64 y y)))))
	21.6b	-1

Compiler

Compiled 1734 to 466 computations (73.1% saved)

localize7.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (/.f64 (+.f64 x y) (hypot.f64 x y)))
✓	0.0b	(/.f64 (-.f64 x y) (hypot.f64 x y))
✓	0.0b	(/.f64 (+.f64 x y) (hypot.f64 x y))

series48.0ms (1.9%)

Counts

3 → 72

Calls

3 calls:

26.0ms	(*.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (/.f64 (+.f64 x y) (hypot.f64 x y)))
11.0ms	(/.f64 (+.f64 x y) (hypot.f64 x y))
10.0ms	(/.f64 (-.f64 x y) (hypot.f64 x y))

rewrite35.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

67×	`*-un-lft-identity_binary64`
65×	`add-sqr-sqrt_binary64`
58×	`times-frac_binary64`
39×	`add-cube-cbrt_binary64`
19×	`associate-l_binary64`

Counts

3 → 136

Calls

3 calls:

14.0ms	(*.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (/.f64 (+.f64 x y) (hypot.f64 x y)))
5.0ms	(/.f64 (+.f64 x y) (hypot.f64 x y))
5.0ms	(/.f64 (-.f64 x y) (hypot.f64 x y))

simplify104.0ms (4.3%)

Algorithm

1×	egg-herbie

Rules

614×	`times-frac_binary64`
493×	`distribute-rgt-in_binary64`
464×	`fma-def_binary64`
222×	`cancel-sign-sub-inv_binary64`
176×	`sub-neg_binary64`

Counts

208 → 233

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	240	4519
1	735	4135
2	2321	4033
3	5136	4033

prune125.0ms (5.1%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	230	3	233
Fresh	1	1	2
Picked	1	0	1
Done	0	0	0
Total	232	4	236

Error

Counts

236 → 4

Alt Table

Status	Error	Program
	20.1b	(log1p.f64 (expm1.f64 (/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (fma.f64 x x (.f64 y y)))))
	41.5b	(fma.f64 (*.f64 (/.f64 y x) (/.f64 y x)) -2 1)
▶	0.0b	(*.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (log1p.f64 (expm1.f64 (/.f64 (+.f64 x y) (hypot.f64 x y)))))
	20.8b	(fma.f64 2 (*.f64 (/.f64 x y) (/.f64 x y)) -1)

Compiler

Compiled 5801 to 1184 computations (79.6% saved)

localize12.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (log1p.f64 (expm1.f64 (/.f64 (+.f64 x y) (hypot.f64 x y)))))
✓	0.0b	(log1p.f64 (expm1.f64 (/.f64 (+.f64 x y) (hypot.f64 x y))))
	0.0b	(/.f64 (+.f64 x y) (hypot.f64 x y))
✓	0.6b	(expm1.f64 (/.f64 (+.f64 x y) (hypot.f64 x y)))

series60.0ms (2.4%)

Counts

3 → 72

Calls

3 calls:

28.0ms

(*.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (log1p.f64 (expm1.f64 (/.f64 (+.f64 x y) (hypot.f64 x y)))))

20.0ms

(expm1.f64 (/.f64 (+.f64 x y) (hypot.f64 x y)))

11.0ms

(log1p.f64 (expm1.f64 (/.f64 (+.f64 x y) (hypot.f64 x y))))

rewrite13.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`add-sqr-sqrt_binary64`
19×	`associate-l_binary64`
19×	`*-un-lft-identity_binary64`
16×	`times-frac_binary64`
13×	`add-cube-cbrt_binary64`

Counts

3 → 62

Calls

3 calls:

7.0ms

(*.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (log1p.f64 (expm1.f64 (/.f64 (+.f64 x y) (hypot.f64 x y)))))

0.0ms

(expm1.f64 (/.f64 (+.f64 x y) (hypot.f64 x y)))

0.0ms

(log1p.f64 (expm1.f64 (/.f64 (+.f64 x y) (hypot.f64 x y))))

simplify98.0ms (4%)

Algorithm

1×	egg-herbie

Rules

990×	`times-frac_binary64`
486×	`fma-neg_binary64`
341×	`fma-def_binary64`
272×	`cancel-sign-sub-inv_binary64`
214×	`sub-neg_binary64`

Counts

134 → 161

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	219	3044
1	605	2776
2	2000	2632
3	4685	2620
4	4998	2620

prune144.0ms (5.8%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	222	0	222
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	222	4	226

Error

Counts

226 → 4

Alt Table

Status	Error	Program
▶	20.1b	(log1p.f64 (expm1.f64 (/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (fma.f64 x x (.f64 y y)))))
	41.5b	(fma.f64 (*.f64 (/.f64 y x) (/.f64 y x)) -2 1)
✓	0.0b	(*.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (log1p.f64 (expm1.f64 (/.f64 (+.f64 x y) (hypot.f64 x y)))))
	20.8b	(fma.f64 2 (*.f64 (/.f64 x y) (/.f64 x y)) -1)

Compiler

Compiled 5614 to 1554 computations (72.3% saved)

localize12.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(fma.f64 x x (*.f64 y y))
✓	0.0b	(log1p.f64 (expm1.f64 (/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (fma.f64 x x (.f64 y y)))))
✓	0.3b	(expm1.f64 (/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (fma.f64 x x (.f64 y y))))
	19.8b	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (fma.f64 x x (.f64 y y)))

series52.0ms (2.1%)

Counts

2 → 48

Calls

2 calls:

34.0ms	(expm1.f64 (/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (fma.f64 x x (.f64 y y))))
19.0ms	(log1p.f64 (expm1.f64 (/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (fma.f64 x x (.f64 y y)))))

rewrite2.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`log1p-expm1-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	(expm1.f64 (/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (fma.f64 x x (.f64 y y))))
0.0ms	(log1p.f64 (expm1.f64 (/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (fma.f64 x x (.f64 y y)))))

simplify77.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

737×	`fma-neg_binary64`
366×	`times-frac_binary64`
277×	`distribute-neg-frac_binary64`
238×	`associate-/l*_binary64`
233×	`associate-/r*_binary64`

Counts

70 → 60

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	104	1942
1	269	1772
2	839	1718
3	3565	1706
4	5120	1706

prune80.0ms (3.3%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	136	0	136
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	136	4	140

Error

Counts

140 → 4

Alt Table

Status	Error	Program
✓	20.1b	(log1p.f64 (expm1.f64 (/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (fma.f64 x x (.f64 y y)))))
	41.5b	(fma.f64 (*.f64 (/.f64 y x) (/.f64 y x)) -2 1)
✓	0.0b	(*.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (log1p.f64 (expm1.f64 (/.f64 (+.f64 x y) (hypot.f64 x y)))))
	20.8b	(fma.f64 2 (*.f64 (/.f64 x y) (/.f64 x y)) -1)

Compiler

Compiled 3192 to 1081 computations (66.1% saved)

regimes83.0ms (3.4%)

Accuracy

Total 0.0b remaining (70.9%)

Threshold costs 0.0b (70.9%)

Counts

31 → 1

Compiler

Compiled 1431 to 841 computations (41.2% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3×	`+-commutative_binary64`
2×	`*-commutative_binary64`
2×	`sub-neg_binary64`
1×	`neg-sub0_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	22
1	13	22
2	18	22
3	20	22
4	21	22
5	21	22

end0.0ms (0%)

Compiler: Compiled 17 to 8 computations (52.9% saved)

sample941.0ms (38.3%)

Algorithm

1×

intervals

Results

411.0ms	8000×	body	128	valid
189.0ms	8000×	pre	128	true

Compiler

Compiled 108 to 61 computations (43.5% saved)

Details

analyze55.0ms (2.2%)

sample279.0ms (11.4%)

simplify82.0ms (3.3%)

prune3.0ms (0.1%)

localize8.0ms (0.3%)

series25.0ms (1%)

rewrite11.0ms (0.5%)

simplify61.0ms (2.5%)

prune39.0ms (1.6%)

localize7.0ms (0.3%)

series48.0ms (1.9%)

rewrite35.0ms (1.4%)

simplify104.0ms (4.3%)

prune125.0ms (5.1%)

localize12.0ms (0.5%)

series60.0ms (2.4%)

rewrite13.0ms (0.5%)

simplify98.0ms (4%)

prune144.0ms (5.8%)

localize12.0ms (0.5%)

series52.0ms (2.1%)

rewrite2.0ms (0.1%)

simplify77.0ms (3.1%)

prune80.0ms (3.3%)

regimes83.0ms (3.4%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample941.0ms (38.3%)

Profiling