Details

analyze383.0ms (8%)

Algorithm

1×

Search

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

Compiler

Compiled 11 to 8 computations (27.3% saved)

sample3.1s (65.1%)

Results

1.5s	2562×	body	1024	valid
727.0ms	1274×	body	2048	valid
472.0ms	1261×	body	512	valid
274.0ms	2457×	body	128	valid
147.0ms	667×	body	256	valid
24.0ms	35×	body	4096	valid

Compiler

Compiled 22 to 16 computations (27.3% saved)

preprocess13.0ms (0.3%)

Algorithm

2×	egg-herbie

Rules

2×	`+-commutative_binary64`
1×	`1-exp_binary64`
1×	`hypot-1-def_binary64`
1×	`fma-def_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	12
1	13	9
2	14	9
0	1	1

Stop Event

1×	saturated
1×	saturated

Compiler

Compiled 10 to 7 computations (30% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
1×	`1-exp_binary64`
1×	`hypot-1-def_binary64`
1×	`fma-def_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	12
1	13	9
2	14	9

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

43.2b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	43.2b	(log.f64 (+.f64 x (hypot.f64 1 x)))

Compiler

Compiled 30 to 21 computations (30% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(hypot.f64 1 x)
✓	0.2b	(+.f64 x (hypot.f64 1 x))
✓	2.0b	(log.f64 (+.f64 x (hypot.f64 1 x)))

series8.0ms (0.2%)

Counts

3 → 36

Calls

9 calls:

1.0ms	(log.f64 (+.f64 x (hypot.f64 1 x)))	x	-inf
1.0ms	(log.f64 (+.f64 x (hypot.f64 1 x)))	x	0
1.0ms	(log.f64 (+.f64 x (hypot.f64 1 x)))	x	inf
1.0ms	(+.f64 x (hypot.f64 1 x))	x	-inf
1.0ms	(hypot.f64 1 x)	x	0

rewrite42.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

575×	`log1p-expm1-u_binary64`
575×	`expm1-log1p-u_binary64`
462×	`prod-diff_binary64`
165×	`fma-def_binary64`
105×	`expm1-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	20
1	121	20
2	1537	20

Stop Event

1×	node limit

Counts

3 → 81

simplify35.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

447×	`cancel-sign-sub-inv_binary64`
436×	`fma-neg_binary64`
413×	`associate-/r*_binary64`
338×	`sub-neg_binary64`
314×	`fma-def_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	98	569
1	306	549
2	863	537
3	2779	537

Stop Event

1×	node limit

Counts

117 → 145

prune76.0ms (1.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	141	4	145
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	141	5	146

Error

0.0b

Counts

146 → 5

Alt Table

Status	Error	Program
▶	33.8b	(+.f64 x (fma.f64 3/40 (pow.f64 x 5) (fma.f64 (pow.f64 x 3) -1/6 (*.f64 (pow.f64 x 7) -5/112))))
	44.1b	(pow.f64 (sqrt.f64 (log.f64 (+.f64 x (hypot.f64 1 x)))) 2)
	47.7b	(log.f64 (+.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 -1/2 x) (/.f64 -1/16 (pow.f64 x 5)))))
✓	43.2b	(log.f64 (+.f64 x (hypot.f64 1 x)))
	47.8b	(+.f64 (log.f64 (/.f64 -1 x)) (+.f64 (+.f64 (/.f64 3/32 (pow.f64 x 4)) (log.f64 1/2)) (/.f64 -1/4 (*.f64 x x))))

Compiler

Compiled 2002 to 1496 computations (25.3% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (fma.f64 3/40 (pow.f64 x 5) (fma.f64 (pow.f64 x 3) -1/6 (*.f64 (pow.f64 x 7) -5/112))))
✓	0.0b	(*.f64 (pow.f64 x 7) -5/112)
✓	0.1b	(fma.f64 (pow.f64 x 3) -1/6 (*.f64 (pow.f64 x 7) -5/112))
✓	23.6b	(fma.f64 3/40 (pow.f64 x 5) (fma.f64 (pow.f64 x 3) -1/6 (*.f64 (pow.f64 x 7) -5/112)))

series16.0ms (0.3%)

Counts

4 → 48

Calls

12 calls:

2.0ms	(fma.f64 (pow.f64 x 3) -1/6 (*.f64 (pow.f64 x 7) -5/112))	x	-inf
2.0ms	(fma.f64 (pow.f64 x 3) -1/6 (*.f64 (pow.f64 x 7) -5/112))	x	inf
1.0ms	(fma.f64 3/40 (pow.f64 x 5) (fma.f64 (pow.f64 x 3) -1/6 (*.f64 (pow.f64 x 7) -5/112)))	x	inf
1.0ms	(fma.f64 3/40 (pow.f64 x 5) (fma.f64 (pow.f64 x 3) -1/6 (*.f64 (pow.f64 x 7) -5/112)))	x	-inf
1.0ms	(fma.f64 3/40 (pow.f64 x 5) (fma.f64 (pow.f64 x 3) -1/6 (*.f64 (pow.f64 x 7) -5/112)))	x	0

rewrite66.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

673×	`prod-diff_binary64`
156×	`add-sqr-sqrt_binary64`
152×	`log1p-expm1-u_binary64`
152×	`expm1-log1p-u_binary64`
149×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	66
1	330	66
2	3766	66

Stop Event

1×	node limit

Counts

4 → 95

simplify53.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

652×	`fma-neg_binary64`
440×	`fma-def_binary64`
420×	`cancel-sign-sub-inv_binary64`
399×	`distribute-rgt-neg-in_binary64`
312×	`distribute-lft-neg-in_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	27	648
1	80	638
2	200	600
3	640	594
4	2057	594
5	3738	594
6	4983	594

Stop Event

1×	node limit

Counts

143 → 113

prune98.0ms (2%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	113	0	113
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	113	5	118

Error

0.0b

Counts

118 → 5

Alt Table

Status	Error	Program
✓	33.8b	(+.f64 x (fma.f64 3/40 (pow.f64 x 5) (fma.f64 (pow.f64 x 3) -1/6 (*.f64 (pow.f64 x 7) -5/112))))
▶	44.1b	(pow.f64 (sqrt.f64 (log.f64 (+.f64 x (hypot.f64 1 x)))) 2)
	47.7b	(log.f64 (+.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 -1/2 x) (/.f64 -1/16 (pow.f64 x 5)))))
✓	43.2b	(log.f64 (+.f64 x (hypot.f64 1 x)))
	47.8b	(+.f64 (log.f64 (/.f64 -1 x)) (+.f64 (+.f64 (/.f64 3/32 (pow.f64 x 4)) (log.f64 1/2)) (/.f64 -1/4 (*.f64 x x))))

Compiler

Compiled 2833 to 2235 computations (21.1% saved)

localize6.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(sqrt.f64 (log.f64 (+.f64 x (hypot.f64 1 x))))
✓	0.2b	(pow.f64 (sqrt.f64 (log.f64 (+.f64 x (hypot.f64 1 x)))) 2)
	0.2b	(+.f64 x (hypot.f64 1 x))
	2.0b	(log.f64 (+.f64 x (hypot.f64 1 x)))

series17.0ms (0.4%)

Counts

2 → 16

Calls

6 calls:

3.0ms	(sqrt.f64 (log.f64 (+.f64 x (hypot.f64 1 x))))	x	inf
3.0ms	(sqrt.f64 (log.f64 (+.f64 x (hypot.f64 1 x))))	x	-inf
3.0ms	(pow.f64 (sqrt.f64 (log.f64 (+.f64 x (hypot.f64 1 x)))) 2)	x	-inf
3.0ms	(pow.f64 (sqrt.f64 (log.f64 (+.f64 x (hypot.f64 1 x)))) 2)	x	inf
3.0ms	(pow.f64 (sqrt.f64 (log.f64 (+.f64 x (hypot.f64 1 x)))) 2)	x	0

rewrite54.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

702×	`log1p-expm1-u_binary64`
702×	`expm1-log1p-u_binary64`
462×	`prod-diff_binary64`
77×	`add-sqr-sqrt_binary64`
74×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	20
1	185	20
2	1958	20

Stop Event

1×	node limit

Counts

2 → 46

simplify46.0ms (1%)

Algorithm

1×	egg-herbie

Rules

455×	`sub-neg_binary64`
439×	`fma-def_binary64`
265×	`cancel-sign-sub-inv_binary64`
235×	`associate-+l+_binary64`
215×	`associate--l+_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	107	880
1	326	779
2	1106	739
3	4631	739

Stop Event

1×	node limit

Counts

62 → 76

prune119.0ms (2.5%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	181	1	182
Fresh	0	2	2
Picked	1	0	1
Done	0	2	2
Total	182	5	187

Error

0.0b

Counts

187 → 5

Alt Table

Status	Error	Program
✓	33.8b	(+.f64 x (fma.f64 3/40 (pow.f64 x 5) (fma.f64 (pow.f64 x 3) -1/6 (*.f64 (pow.f64 x 7) -5/112))))
	54.5b	(-.f64 (log.f64 (+.f64 (pow.f64 x 3) (pow.f64 (hypot.f64 1 x) 3))) (log.f64 (fma.f64 x x (*.f64 (hypot.f64 1 x) (-.f64 (hypot.f64 1 x) x)))))
▶	47.7b	(log.f64 (+.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 -1/2 x) (/.f64 -1/16 (pow.f64 x 5)))))
✓	43.2b	(log.f64 (+.f64 x (hypot.f64 1 x)))
	47.8b	(+.f64 (log.f64 (/.f64 -1 x)) (+.f64 (+.f64 (/.f64 3/32 (pow.f64 x 4)) (log.f64 1/2)) (/.f64 -1/4 (*.f64 x x))))

Compiler

Compiled 3586 to 2887 computations (19.5% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 -1/16 (pow.f64 x 5))
✓	0.1b	(/.f64 1/8 (pow.f64 x 3))
✓	11.6b	(log.f64 (+.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 -1/2 x) (/.f64 -1/16 (pow.f64 x 5)))))
✓	17.3b	(+.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 -1/2 x) (/.f64 -1/16 (pow.f64 x 5))))

series13.0ms (0.3%)

Counts

4 → 24

Calls

12 calls:

1.0ms	(+.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 -1/2 x) (/.f64 -1/16 (pow.f64 x 5))))	x	0
1.0ms	(log.f64 (+.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 -1/2 x) (/.f64 -1/16 (pow.f64 x 5)))))	x	0
1.0ms	(log.f64 (+.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 -1/2 x) (/.f64 -1/16 (pow.f64 x 5)))))	x	-inf
1.0ms	(log.f64 (+.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 -1/2 x) (/.f64 -1/16 (pow.f64 x 5)))))	x	inf
1.0ms	(+.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 -1/2 x) (/.f64 -1/16 (pow.f64 x 5))))	x	-inf

rewrite76.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

297×	`log1p-udef_binary64`
170×	`log1p-expm1-u_binary64`
170×	`expm1-log1p-u_binary64`
169×	`add-sqr-sqrt_binary64`
168×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	60
1	357	52
2	5000	52

Stop Event

1×	node limit

Counts

4 → 123

simplify31.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

883×	`fma-def_binary64`
313×	`associate-/r*_binary64`
306×	`associate-l_binary64`
236×	`sub-neg_binary64`
220×	`associate-r_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	75	467
1	221	459
2	589	457
3	1816	451

Stop Event

1×	node limit

Counts

147 → 154

prune114.0ms (2.4%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	154	0	154
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	154	5	159

Error

0.0b

Counts

159 → 5

Alt Table

Status	Error	Program
✓	33.8b	(+.f64 x (fma.f64 3/40 (pow.f64 x 5) (fma.f64 (pow.f64 x 3) -1/6 (*.f64 (pow.f64 x 7) -5/112))))
	54.5b	(-.f64 (log.f64 (+.f64 (pow.f64 x 3) (pow.f64 (hypot.f64 1 x) 3))) (log.f64 (fma.f64 x x (*.f64 (hypot.f64 1 x) (-.f64 (hypot.f64 1 x) x)))))
✓	47.7b	(log.f64 (+.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 -1/2 x) (/.f64 -1/16 (pow.f64 x 5)))))
✓	43.2b	(log.f64 (+.f64 x (hypot.f64 1 x)))
	47.8b	(+.f64 (log.f64 (/.f64 -1 x)) (+.f64 (+.f64 (/.f64 3/32 (pow.f64 x 4)) (log.f64 1/2)) (/.f64 -1/4 (*.f64 x x))))

Compiler

Compiled 3795 to 3070 computations (19.1% saved)

regimes215.0ms (4.5%)

Accuracy

Total 0.0b remaining (60%)

Threshold costs 0.0b (60%)

Counts

49 → 3

Compiler

Compiled 1947 to 1504 computations (22.8% saved)

bsearch38.0ms (0.8%)

Algorithm

2×	binary-search

Calls

2 calls:

21.0ms	x
15.0ms	x

Steps

Iters	Point		Range
0.02282397791680572	∈ [	1.0953671046120256e-6	,	0.06958355100113699	]
-1.097757394967845	∈ [	-373.60856981001484	,	-0.0035811007973851052	]

Compiler

Compiled 2 to 1 computations (50% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	63
1	39	63

Stop Event

1×

saturated

end118.0ms (2.5%)

Stop Event

1×

fuel

Compiler

Compiled 177 to 135 computations (23.7% saved)

Details

analyze383.0ms (8%)

sample3.1s (65.1%)

preprocess13.0ms (0.3%)

simplify6.0ms (0.1%)

prune3.0ms (0.1%)

localize6.0ms (0.1%)

series8.0ms (0.2%)

rewrite42.0ms (0.9%)

simplify35.0ms (0.7%)

prune76.0ms (1.6%)

localize12.0ms (0.2%)

series16.0ms (0.3%)

rewrite66.0ms (1.4%)

simplify53.0ms (1.1%)

prune98.0ms (2%)

localize6.0ms (0.1%)

series17.0ms (0.4%)

rewrite54.0ms (1.1%)

simplify46.0ms (1%)

prune119.0ms (2.5%)

localize10.0ms (0.2%)

series13.0ms (0.3%)

rewrite76.0ms (1.6%)

simplify31.0ms (0.7%)

prune114.0ms (2.4%)

regimes215.0ms (4.5%)

bsearch38.0ms (0.8%)

simplify3.0ms (0.1%)

end118.0ms (2.5%)

Profiling