Details

analyze402.0ms (8.5%)

Algorithm

1×

Search

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

Compiler

Compiled 11 to 8 computations (27.3% saved)

sample3.3s (69.4%)

Results

1.5s	2558×	body	1024	valid
776.0ms	1297×	body	2048	valid
493.0ms	1290×	body	512	valid
272.0ms	2406×	body	128	valid
162.0ms	672×	body	256	valid
24.0ms	33×	body	4096	valid

Compiler

Compiled 22 to 16 computations (27.3% saved)

preprocess17.0ms (0.4%)

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

46.9b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	46.9b	(log.f64 (+.f64 x (hypot.f64 1 x)))

Compiler

Compiled 30 to 21 computations (30% saved)

localize4.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(hypot.f64 1 x)
✓	0.6b	(+.f64 x (hypot.f64 1 x))
✓	3.0b	(log.f64 (+.f64 x (hypot.f64 1 x)))

series10.0ms (0.2%)

Counts

3 → 36

Calls

9 calls:

3.0ms	(+.f64 x (hypot.f64 1 x))	x	-inf
1.0ms	(log.f64 (+.f64 x (hypot.f64 1 x)))	x	-inf
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	(+.f64 x (hypot.f64 1 x))	x	inf

rewrite43.0ms (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

simplify38.0ms (0.8%)

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

prune69.0ms (1.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	142	3	145
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	142	4	146

Error

Counts

146 → 4

Alt Table

Status	Error	Program
	46.7b	(log.f64 (+.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 -1/2 x) (/.f64 -1/16 (pow.f64 x 5)))))
	46.8b	(-.f64 (+.f64 (.f64 3/32 (/.f64 1 (pow.f64 x 4))) (+.f64 (log.f64 (/.f64 -1 x)) (log.f64 1/2))) (.f64 1/4 (/.f64 1 (pow.f64 x 2))))
▶	31.1b	(fma.f64 (pow.f64 x 3) -1/6 x)
✓	46.9b	(log.f64 (+.f64 x (hypot.f64 1 x)))

Compiler

Compiled 1968 to 1472 computations (25.2% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 (pow.f64 x 3) -1/6 x)

series3.0ms (0.1%)

Counts

1 → 12

Calls

3 calls:

1.0ms	(fma.f64 (pow.f64 x 3) -1/6 x)	x	-inf
1.0ms	(fma.f64 (pow.f64 x 3) -1/6 x)	x	inf
1.0ms	(fma.f64 (pow.f64 x 3) -1/6 x)	x	0

rewrite32.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

493×	`log1p-expm1-u_binary64`
493×	`expm1-log1p-u_binary64`
282×	`unpow-prod-down_binary64`
223×	`log-prod_binary64`
142×	`pow2_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	126	8
2	1355	8

Stop Event

1×	node limit

Counts

1 → 36

simplify29.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

1047×	`fma-def_binary64`
818×	`unswap-sqr_binary64`
241×	`associate-l_binary64`
194×	`fma-neg_binary64`
174×	`associate-r_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	9	105
1	23	105
2	61	87
3	194	87
4	429	87
5	1190	87
6	2374	87
7	3266	87

Stop Event

1×	node limit

Counts

48 → 41

prune21.0ms (0.4%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	41	0	41
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	41	4	45

Error

Counts

45 → 4

Alt Table

Status	Error	Program
▶	46.7b	(log.f64 (+.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 -1/2 x) (/.f64 -1/16 (pow.f64 x 5)))))
	46.8b	(-.f64 (+.f64 (.f64 3/32 (/.f64 1 (pow.f64 x 4))) (+.f64 (log.f64 (/.f64 -1 x)) (log.f64 1/2))) (.f64 1/4 (/.f64 1 (pow.f64 x 2))))
✓	31.1b	(fma.f64 (pow.f64 x 3) -1/6 x)
✓	46.9b	(log.f64 (+.f64 x (hypot.f64 1 x)))

Compiler

Compiled 597 to 468 computations (21.6% saved)

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 1/8 (pow.f64 x 3))
✓	0.1b	(/.f64 -1/16 (pow.f64 x 5))
✓	13.8b	(log.f64 (+.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 -1/2 x) (/.f64 -1/16 (pow.f64 x 5)))))
✓	19.1b	(+.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

rewrite81.0ms (1.7%)

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

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	154	0	154
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	154	4	158

Error

Counts

158 → 4

Alt Table

Status	Error	Program
✓	46.7b	(log.f64 (+.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 -1/2 x) (/.f64 -1/16 (pow.f64 x 5)))))
▶	46.8b	(-.f64 (+.f64 (.f64 3/32 (/.f64 1 (pow.f64 x 4))) (+.f64 (log.f64 (/.f64 -1 x)) (log.f64 1/2))) (.f64 1/4 (/.f64 1 (pow.f64 x 2))))
✓	31.1b	(fma.f64 (pow.f64 x 3) -1/6 x)
✓	46.9b	(log.f64 (+.f64 x (hypot.f64 1 x)))

Compiler

Compiled 3787 to 3069 computations (19% saved)

localize17.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(+.f64 (log.f64 (/.f64 -1 x)) (log.f64 1/2))
✓	0.4b	(/.f64 1 (pow.f64 x 2))
✓	0.5b	(/.f64 1 (pow.f64 x 4))
✓	7.4b	(-.f64 (+.f64 (.f64 3/32 (/.f64 1 (pow.f64 x 4))) (+.f64 (log.f64 (/.f64 -1 x)) (log.f64 1/2))) (.f64 1/4 (/.f64 1 (pow.f64 x 2))))

series56.0ms (1.2%)

Counts

4 → 18

Calls

12 calls:

18.0ms	(+.f64 (log.f64 (/.f64 -1 x)) (log.f64 1/2))	x	0
15.0ms	(+.f64 (log.f64 (/.f64 -1 x)) (log.f64 1/2))	x	-inf
12.0ms	(+.f64 (log.f64 (/.f64 -1 x)) (log.f64 1/2))	x	inf
2.0ms	(-.f64 (+.f64 (.f64 3/32 (/.f64 1 (pow.f64 x 4))) (+.f64 (log.f64 (/.f64 -1 x)) (log.f64 1/2))) (.f64 1/4 (/.f64 1 (pow.f64 x 2))))	x	inf
2.0ms	(-.f64 (+.f64 (.f64 3/32 (/.f64 1 (pow.f64 x 4))) (+.f64 (log.f64 (/.f64 -1 x)) (log.f64 1/2))) (.f64 1/4 (/.f64 1 (pow.f64 x 2))))	x	-inf

rewrite44.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

212×	`log1p-expm1-u_binary64`
212×	`expm1-log1p-u_binary64`
209×	`add-sqr-sqrt_binary64`
209×	`add-cbrt-cube_binary64`
203×	`add-log-exp_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	21	42
1	476	36

Stop Event

1×	node limit

Counts

4 → 130

simplify28.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

482×	`fma-def_binary64`
418×	`fma-neg_binary64`
374×	`cancel-sign-sub-inv_binary64`
370×	`associate-/r*_binary64`
294×	`sub-neg_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	37	297
1	93	289
2	244	289
3	704	289
4	1967	289

Stop Event

1×	node limit

Counts

148 → 143

prune99.0ms (2.1%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	143	0	143
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	143	4	147

Error

Counts

147 → 4

Alt Table

Status	Error	Program
✓	46.7b	(log.f64 (+.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 -1/2 x) (/.f64 -1/16 (pow.f64 x 5)))))
✓	46.8b	(-.f64 (+.f64 (.f64 3/32 (/.f64 1 (pow.f64 x 4))) (+.f64 (log.f64 (/.f64 -1 x)) (log.f64 1/2))) (.f64 1/4 (/.f64 1 (pow.f64 x 2))))
✓	31.1b	(fma.f64 (pow.f64 x 3) -1/6 x)
✓	46.9b	(log.f64 (+.f64 x (hypot.f64 1 x)))

Compiler

Compiled 3843 to 3159 computations (17.8% saved)

regimes137.0ms (2.9%)

Accuracy

Total 0.1b remaining (52.5%)

Threshold costs 0.1b (52.5%)

Counts

35 → 3

Compiler

Compiled 1578 to 1255 computations (20.5% saved)

bsearch40.0ms (0.9%)

Algorithm

2×	binary-search

Calls

2 calls:

21.0ms	x
18.0ms	x

Steps

Iters	Point		Range
0.0009468969774314637	∈ [	3.0806495832780393e-7	,	19034.37601013665	]
-1.0296531942022684	∈ [	-373.60856981001484	,	-8.738875892567779e-6	]

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	28	49
1	31	49

Stop Event

1×

saturated

end86.0ms (1.8%)

Stop Event

1×

done

Compiler

Compiled 125 to 97 computations (22.4% saved)

Details

analyze402.0ms (8.5%)

sample3.3s (69.4%)

preprocess17.0ms (0.4%)

simplify6.0ms (0.1%)

prune3.0ms (0.1%)

localize4.0ms (0.1%)

series10.0ms (0.2%)

rewrite43.0ms (0.9%)

simplify38.0ms (0.8%)

prune69.0ms (1.5%)

localize4.0ms (0.1%)

series3.0ms (0.1%)

rewrite32.0ms (0.7%)

simplify29.0ms (0.6%)

prune21.0ms (0.4%)

localize12.0ms (0.3%)

series13.0ms (0.3%)

rewrite81.0ms (1.7%)

simplify31.0ms (0.7%)

prune114.0ms (2.4%)

localize17.0ms (0.4%)

series56.0ms (1.2%)

rewrite44.0ms (0.9%)

simplify28.0ms (0.6%)

prune99.0ms (2.1%)

regimes137.0ms (2.9%)

bsearch40.0ms (0.9%)

simplify3.0ms (0.1%)

end86.0ms (1.8%)

Profiling