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)

sample2.1s (50%)

Results

1.0s	2165×	body	2048	valid
474.0ms	4280×	body	128	valid
386.0ms	1027×	body	1024	valid
148.0ms	539×	body	512	valid
44.0ms	245×	body	256	valid

Compiler

Compiled 28 to 26 computations (7.1% saved)

preprocess17.0ms (0.4%)

Algorithm

2×	egg-herbie

Rules

8×	`sub-neg_binary64`
8×	`fma-def_binary64`
5×	`+-commutative_binary64`
3×	`*-commutative_binary64`
3×	`associate-+l-_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	18
1	22	15
2	29	15
3	37	15
4	44	15
5	54	15
6	65	15
7	77	15
8	80	15
0	1	1

Stop Event

1×	saturated
1×	saturated

Compiler

Compiled 13 to 12 computations (7.7% saved)

simplify8.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

8×	`sub-neg_binary64`
8×	`fma-def_binary64`
5×	`+-commutative_binary64`
3×	`*-commutative_binary64`
3×	`associate-+l-_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	18
1	22	15
2	29	15
3	37	15
4	44	15
5	54	15
6	65	15
7	77	15
8	80	15

Stop Event

1×

saturated

Counts

1 → 2

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

14.6b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	14.6b	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))

Compiler

Compiled 45 to 41 computations (8.9% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(hypot.f64 1 x)
✓	0.0b	(/.f64 1/2 (hypot.f64 1 x))
✓	1.8b	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))

series11.0ms (0.3%)

Counts

3 → 36

Calls

9 calls:

3.0ms	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))	x	-inf
2.0ms	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))	x	inf
1.0ms	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))	x	0
1.0ms	(/.f64 1/2 (hypot.f64 1 x))	x	-inf
1.0ms	(/.f64 1/2 (hypot.f64 1 x))	x	inf

rewrite48.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

406×	`log-prod_binary64`
387×	`prod-diff_binary64`
205×	`fma-def_binary64`
170×	`expm1-udef_binary64`
169×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	26
1	202	26
2	2576	26

Stop Event

1×	node limit

Counts

3 → 88

simplify41.0ms (1%)

Algorithm

1×	egg-herbie

Rules

715×	`fma-neg_binary64`
414×	`sub-neg_binary64`
347×	`fma-def_binary64`
185×	`associate--l+_binary64`
179×	`associate-r_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	116	670
1	365	652
2	1120	636
3	3998	636

Stop Event

1×	node limit

Counts

124 → 152

prune144.0ms (3.4%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	150	2	152
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	151	2	153

Error

0.0b

Counts

153 → 2

Alt Table

Status	Error	Program
▶	14.1b	(/.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
	33.7b	(-.f64 (+.f64 (.f64 69/1024 (pow.f64 x 6)) (.f64 1/8 (pow.f64 x 2))) (+.f64 (.f64 11/128 (pow.f64 x 4)) (.f64 1843/32768 (pow.f64 x 8))))

Status

Error

Program

▶

14.1b

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

33.7b

(-.f64 (+.f64 (*.f64 69/1024 (pow.f64 x 6)) (*.f64 1/8 (pow.f64 x 2))) (+.f64 (*.f64 11/128 (pow.f64 x 4)) (*.f64 1843/32768 (pow.f64 x 8))))

Compiler

Compiled 2785 to 2461 computations (11.6% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
	0.0b	(hypot.f64 1 x)
	0.0b	(/.f64 1/2 (hypot.f64 1 x))
✓	1.3b	(-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))

series7.0ms (0.2%)

Counts

2 → 24

Calls

6 calls:

2.0ms	(+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))	x	-inf
2.0ms	(+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))	x	inf
1.0ms	(-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))	x	0
1.0ms	(+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))	x	0
1.0ms	(-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))	x	inf

rewrite51.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

474×	`prod-diff_binary64`
311×	`fma-def_binary64`
191×	`expm1-udef_binary64`
191×	`log1p-udef_binary64`
149×	`fma-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	25
1	226	25
2	2967	25

Stop Event

1×	node limit

Counts

2 → 88

simplify34.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

529×	`fma-neg_binary64`
322×	`sub-neg_binary64`
231×	`fma-def_binary64`
206×	`distribute-neg-frac_binary64`
187×	`unswap-sqr_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	89	470
1	285	460
2	890	448
3	3270	448

Stop Event

1×	node limit

Counts

112 → 130

prune273.0ms (6.5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	309	1	310
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	309	3	312

Error

Counts

312 → 3

Alt Table

Status	Error	Program
✓	14.1b	(/.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
	33.7b	(/.f64 (fma.f64 1/4 (.f64 x x) (fma.f64 5/32 (pow.f64 x 6) (fma.f64 (pow.f64 x 4) -3/16 (.f64 (pow.f64 x 8) -35/256)))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
▶	33.7b	(-.f64 (+.f64 (.f64 69/1024 (pow.f64 x 6)) (.f64 1/8 (pow.f64 x 2))) (+.f64 (.f64 11/128 (pow.f64 x 4)) (.f64 1843/32768 (pow.f64 x 8))))

Compiler

Compiled 7917 to 6952 computations (12.2% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 69/1024 (pow.f64 x 6))
✓	0.0b	(*.f64 1843/32768 (pow.f64 x 8))
✓	0.1b	(*.f64 11/128 (pow.f64 x 4))
✓	28.8b	(-.f64 (+.f64 (.f64 69/1024 (pow.f64 x 6)) (.f64 1/8 (pow.f64 x 2))) (+.f64 (.f64 11/128 (pow.f64 x 4)) (.f64 1843/32768 (pow.f64 x 8))))

series15.0ms (0.4%)

Counts

4 → 9

Calls

12 calls:

1.0ms	(-.f64 (+.f64 (.f64 69/1024 (pow.f64 x 6)) (.f64 1/8 (pow.f64 x 2))) (+.f64 (.f64 11/128 (pow.f64 x 4)) (.f64 1843/32768 (pow.f64 x 8))))	x	inf
1.0ms	(-.f64 (+.f64 (.f64 69/1024 (pow.f64 x 6)) (.f64 1/8 (pow.f64 x 2))) (+.f64 (.f64 11/128 (pow.f64 x 4)) (.f64 1843/32768 (pow.f64 x 8))))	x	-inf
1.0ms	(-.f64 (+.f64 (.f64 69/1024 (pow.f64 x 6)) (.f64 1/8 (pow.f64 x 2))) (+.f64 (.f64 11/128 (pow.f64 x 4)) (.f64 1843/32768 (pow.f64 x 8))))	x	0
1.0ms	(*.f64 69/1024 (pow.f64 x 6))	x	inf
1.0ms	(*.f64 69/1024 (pow.f64 x 6))	x	-inf

rewrite41.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

214×	`log1p-expm1-u_binary64`
214×	`expm1-log1p-u_binary64`
210×	`add-cbrt-cube_binary64`
207×	`add-sqr-sqrt_binary64`
201×	`add-cube-cbrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	51
1	470	51

Stop Event

1×	node limit

Counts

4 → 82

simplify28.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

707×	`distribute-rgt-neg-in_binary64`
558×	`associate-l_binary64`
413×	`unswap-sqr_binary64`
406×	`associate-r_binary64`
279×	`fma-def_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	26	138
1	68	130
2	161	126
3	563	126
4	3490	126

Stop Event

1×	node limit

Counts

91 → 93

prune100.0ms (2.4%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	93	0	93
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	93	3	96

Error

Counts

96 → 3

Alt Table

Status	Error	Program
✓	14.1b	(/.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
▶	33.7b	(/.f64 (fma.f64 1/4 (.f64 x x) (fma.f64 5/32 (pow.f64 x 6) (fma.f64 (pow.f64 x 4) -3/16 (.f64 (pow.f64 x 8) -35/256)))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
✓	33.7b	(-.f64 (+.f64 (.f64 69/1024 (pow.f64 x 6)) (.f64 1/8 (pow.f64 x 2))) (+.f64 (.f64 11/128 (pow.f64 x 4)) (.f64 1843/32768 (pow.f64 x 8))))

Compiler

Compiled 3374 to 2667 computations (21% saved)

localize19.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (pow.f64 x 8) -35/256)
✓	0.1b	(fma.f64 (pow.f64 x 4) -3/16 (*.f64 (pow.f64 x 8) -35/256))
✓	16.0b	(fma.f64 1/4 (.f64 x x) (fma.f64 5/32 (pow.f64 x 6) (fma.f64 (pow.f64 x 4) -3/16 (.f64 (pow.f64 x 8) -35/256))))
✓	28.8b	(fma.f64 5/32 (pow.f64 x 6) (fma.f64 (pow.f64 x 4) -3/16 (*.f64 (pow.f64 x 8) -35/256)))

series15.0ms (0.4%)

Counts

4 → 48

Calls

12 calls:

1.0ms	(fma.f64 (pow.f64 x 4) -3/16 (*.f64 (pow.f64 x 8) -35/256))	x	inf
1.0ms	(fma.f64 (pow.f64 x 4) -3/16 (*.f64 (pow.f64 x 8) -35/256))	x	-inf
1.0ms	(fma.f64 5/32 (pow.f64 x 6) (fma.f64 (pow.f64 x 4) -3/16 (*.f64 (pow.f64 x 8) -35/256)))	x	-inf
1.0ms	(fma.f64 5/32 (pow.f64 x 6) (fma.f64 (pow.f64 x 4) -3/16 (*.f64 (pow.f64 x 8) -35/256)))	x	inf
1.0ms	(fma.f64 5/32 (pow.f64 x 6) (fma.f64 (pow.f64 x 4) -3/16 (*.f64 (pow.f64 x 8) -35/256)))	x	0

rewrite54.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

258×	`expm1-udef_binary64`
258×	`log1p-udef_binary64`
201×	`prod-diff_binary64`
158×	`log1p-expm1-u_binary64`
158×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	70
1	360	70
2	3650	70

Stop Event

1×	node limit

Counts

4 → 84

simplify40.0ms (1%)

Algorithm

1×	egg-herbie

Rules

621×	`associate-l_binary64`
475×	`fma-def_binary64`
413×	`unswap-sqr_binary64`
399×	`associate-r_binary64`
315×	`fma-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	31	684
1	82	670
2	200	630
3	712	630
4	4314	630

Stop Event

1×	node limit

Counts

132 → 103

prune114.0ms (2.7%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	103	0	103
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	103	3	106

Error

Counts

106 → 3

Alt Table

Status	Error	Program
✓	14.1b	(/.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
✓	33.7b	(/.f64 (fma.f64 1/4 (.f64 x x) (fma.f64 5/32 (pow.f64 x 6) (fma.f64 (pow.f64 x 4) -3/16 (.f64 (pow.f64 x 8) -35/256)))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
✓	33.7b	(-.f64 (+.f64 (.f64 69/1024 (pow.f64 x 6)) (.f64 1/8 (pow.f64 x 2))) (+.f64 (.f64 11/128 (pow.f64 x 4)) (.f64 1843/32768 (pow.f64 x 8))))

Compiler

Compiled 3736 to 2959 computations (20.8% saved)

regimes904.0ms (21.5%)

Accuracy

Total 0.0b remaining (29.2%)

Threshold costs 0.0b (29.2%)

Counts

114 → 2

Compiler

Compiled 13525 to 11920 computations (11.9% saved)

bsearch4.0ms (0.1%)

Algorithm

1×	left-value

Calls

1 calls:

0.0ms

(hypot.f64 1 x)

Steps

Iters	Point		Range
1.0000053276938277	∈ [	1.0000053276938277	,	5.155564931657496	]

Compiler

Compiled 4 to 3 computations (25% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	66
1	41	66
2	51	66
3	55	66
4	57	66

Stop Event

1×

saturated

end98.0ms (2.3%)

Stop Event

1×

done

Compiler

Compiled 167 to 139 computations (16.8% saved)

Details

analyze1.0ms (0%)

sample2.1s (50%)

preprocess17.0ms (0.4%)

simplify8.0ms (0.2%)

prune3.0ms (0.1%)

localize6.0ms (0.1%)

series11.0ms (0.3%)

rewrite48.0ms (1.1%)

simplify41.0ms (1%)

prune144.0ms (3.4%)

localize9.0ms (0.2%)

series7.0ms (0.2%)

rewrite51.0ms (1.2%)

simplify34.0ms (0.8%)

prune273.0ms (6.5%)

localize13.0ms (0.3%)

series15.0ms (0.4%)

rewrite41.0ms (1%)

simplify28.0ms (0.7%)

prune100.0ms (2.4%)

localize19.0ms (0.5%)

series15.0ms (0.4%)

rewrite54.0ms (1.3%)

simplify40.0ms (1%)

prune114.0ms (2.7%)

regimes904.0ms (21.5%)

bsearch4.0ms (0.1%)

simplify3.0ms (0.1%)

end98.0ms (2.3%)

Profiling