Details

analyze1.2s (17.9%)

Algorithm

1×

Search

True	Other	False	Iter
0%	48.6%	51.4%	0
0%	48.6%	51.4%	1
24.3%	24.3%	51.4%	2
24.3%	24.3%	51.4%	3
30.4%	18.2%	51.4%	4
30.4%	18.2%	51.4%	5
33.4%	15.2%	51.4%	6
33.4%	15.2%	51.4%	7
34.6%	14.1%	51.4%	8
34.8%	13.9%	51.4%	9
35.4%	13.2%	51.4%	10
35.6%	13.1%	51.4%	11
35.9%	12.7%	51.4%	12
36%	12.6%	51.4%	13
36.2%	12.4%	51.4%	14

Compiler

Compiled 28 to 20 computations (28.6% saved)

sample2.0s (31.6%)

Results

922.0ms	6293×	body	128	valid
482.0ms	782×	body	2048	valid
267.0ms	512×	body	1024	valid
224.0ms	295×	body	4096	valid
85.0ms	241×	body	512	valid
35.0ms	133×	body	256	valid

Compiler

Compiled 56 to 40 computations (28.6% saved)

preprocess20.0ms (0.3%)

Algorithm

2×	egg-herbie

Rules

18×	`fma-def_binary64`
12×	`*-commutative_binary64`
4×	`+-commutative_binary64`
4×	`associate-/l*_binary64`
4×	`distribute-lft-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	48
1	50	48
2	70	44
3	84	44
4	88	44
5	92	44
6	94	44
0	2	2

Stop Event

1×	saturated
1×	saturated

Compiler

Compiled 19 to 14 computations (26.3% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

9×	`fma-def_binary64`
6×	`*-commutative_binary64`
2×	`+-commutative_binary64`
2×	`associate-/l*_binary64`
2×	`distribute-lft-in_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	15	24
1	31	24
2	41	22
3	48	22
4	50	22
5	52	22
6	53	22

Stop Event

1×

saturated

Counts

1 → 2

prune7.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

12.6b

Counts

3 → 2

Alt Table

Status	Error	Program
	12.6b	(sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (.f64 x x)))))))
▶	12.6b	(sqrt.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 4 (.f64 p p))))) 1/2))

Compiler

Compiled 106 to 76 computations (28.3% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 x (sqrt.f64 (fma.f64 x x (.f64 4 (.f64 p p)))))
✓	0.0b	(.f64 4 (.f64 p p))
✓	0.6b	(fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 4 (.f64 p p))))) 1/2)
✓	14.9b	(sqrt.f64 (fma.f64 x x (.f64 4 (.f64 p p))))

series55.0ms (0.9%)

Counts

4 → 84

Calls

21 calls:

5.0ms	(fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 4 (.f64 p p))))) 1/2)	x	-inf
5.0ms	(/.f64 x (sqrt.f64 (fma.f64 x x (.f64 4 (.f64 p p)))))	x	-inf
5.0ms	(fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 4 (.f64 p p))))) 1/2)	p	0
4.0ms	(/.f64 x (sqrt.f64 (fma.f64 x x (.f64 4 (.f64 p p)))))	x	0
4.0ms	(sqrt.f64 (fma.f64 x x (.f64 4 (.f64 p p))))	x	inf

rewrite52.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

507×	`log-prod_binary64`
192×	`expm1-udef_binary64`
192×	`log1p-udef_binary64`
177×	`pow3_binary64`
174×	`log-pow_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	56
1	228	38
2	2703	38

Stop Event

1×	node limit

Counts

4 → 107

simplify50.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

624×	`times-frac_binary64`
367×	`fma-def_binary64`
324×	`associate-/l*_binary64`
284×	`associate-/r*_binary64`
284×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	129	1708
1	427	1658
2	1389	1608

Stop Event

1×	node limit

Counts

191 → 195

prune204.0ms (3.2%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	190	5	195
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	192	5	197

Error

5.1b

Counts

197 → 5

Alt Table

Status	Error	Program
	13.0b	(sqrt.f64 (+.f64 (log.f64 (sqrt.f64 (exp.f64 (fma.f64 1/2 (/.f64 x (hypot.f64 x (.f64 p 2))) 1/2)))) (log.f64 (sqrt.f64 (exp.f64 (fma.f64 1/2 (/.f64 x (hypot.f64 x (.f64 p 2))) 1/2))))))
	55.2b	(sqrt.f64 (-.f64 (/.f64 (pow.f64 p 2) (pow.f64 x 2)) (*.f64 3 (/.f64 (pow.f64 p 4) (pow.f64 x 4)))))
	12.6b	(sqrt.f64 (fma.f64 1/2 (log1p.f64 (expm1.f64 (/.f64 x (hypot.f64 x (*.f64 p 2))))) 1/2))
▶	12.6b	(sqrt.f64 (expm1.f64 (log1p.f64 (fma.f64 1/2 (/.f64 x (hypot.f64 x (*.f64 p 2))) 1/2))))
	51.6b	(sqrt.f64 (*.f64 (/.f64 p x) (/.f64 p x)))

Compiler

Compiled 3914 to 2886 computations (26.3% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(hypot.f64 x (*.f64 p 2))
✓	0.0b	(/.f64 x (hypot.f64 x (*.f64 p 2)))
✓	0.0b	(expm1.f64 (log1p.f64 (fma.f64 1/2 (/.f64 x (hypot.f64 x (*.f64 p 2))) 1/2)))
✓	0.6b	(fma.f64 1/2 (/.f64 x (hypot.f64 x (*.f64 p 2))) 1/2)

series64.0ms (1%)

Counts

4 → 96

Calls

24 calls:

5.0ms	(fma.f64 1/2 (/.f64 x (hypot.f64 x (*.f64 p 2))) 1/2)	x	inf
5.0ms	(fma.f64 1/2 (/.f64 x (hypot.f64 x (*.f64 p 2))) 1/2)	x	-inf
5.0ms	(expm1.f64 (log1p.f64 (fma.f64 1/2 (/.f64 x (hypot.f64 x (*.f64 p 2))) 1/2)))	x	-inf
4.0ms	(/.f64 x (hypot.f64 x (*.f64 p 2)))	x	inf
3.0ms	(hypot.f64 x (*.f64 p 2))	p	-inf

rewrite53.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

460×	`log-prod_binary64`
257×	`pow2_binary64`
182×	`expm1-udef_binary64`
182×	`log1p-udef_binary64`
180×	`pow1/3_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	45
1	209	45
2	2468	45

Stop Event

1×	node limit

Counts

4 → 129

simplify48.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

624×	`times-frac_binary64`
363×	`fma-def_binary64`
324×	`associate-/l*_binary64`
285×	`associate-/r*_binary64`
284×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	128	2136
1	425	2062
2	1381	1994

Stop Event

1×	node limit

Counts

225 → 189

prune155.0ms (2.4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	189	0	189
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	189	5	194

Error

5.1b

Counts

194 → 5

Alt Table

Status	Error	Program
	13.0b	(sqrt.f64 (+.f64 (log.f64 (sqrt.f64 (exp.f64 (fma.f64 1/2 (/.f64 x (hypot.f64 x (.f64 p 2))) 1/2)))) (log.f64 (sqrt.f64 (exp.f64 (fma.f64 1/2 (/.f64 x (hypot.f64 x (.f64 p 2))) 1/2))))))
	55.2b	(sqrt.f64 (-.f64 (/.f64 (pow.f64 p 2) (pow.f64 x 2)) (*.f64 3 (/.f64 (pow.f64 p 4) (pow.f64 x 4)))))
▶	12.6b	(sqrt.f64 (fma.f64 1/2 (log1p.f64 (expm1.f64 (/.f64 x (hypot.f64 x (*.f64 p 2))))) 1/2))
✓	12.6b	(sqrt.f64 (expm1.f64 (log1p.f64 (fma.f64 1/2 (/.f64 x (hypot.f64 x (*.f64 p 2))) 1/2))))
	51.6b	(sqrt.f64 (*.f64 (/.f64 p x) (/.f64 p x)))

Compiler

Compiled 4129 to 2651 computations (35.8% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(/.f64 x (hypot.f64 x (*.f64 p 2)))
✓	0.0b	(log1p.f64 (expm1.f64 (/.f64 x (hypot.f64 x (*.f64 p 2)))))
✓	0.3b	(expm1.f64 (/.f64 x (hypot.f64 x (*.f64 p 2))))
✓	0.6b	(fma.f64 1/2 (log1p.f64 (expm1.f64 (/.f64 x (hypot.f64 x (*.f64 p 2))))) 1/2)

series53.0ms (0.8%)

Counts

3 → 72

Calls

18 calls:

5.0ms	(log1p.f64 (expm1.f64 (/.f64 x (hypot.f64 x (*.f64 p 2)))))	p	-inf
5.0ms	(fma.f64 1/2 (log1p.f64 (expm1.f64 (/.f64 x (hypot.f64 x (*.f64 p 2))))) 1/2)	x	-inf
4.0ms	(fma.f64 1/2 (log1p.f64 (expm1.f64 (/.f64 x (hypot.f64 x (*.f64 p 2))))) 1/2)	p	0
4.0ms	(expm1.f64 (/.f64 x (hypot.f64 x (*.f64 p 2))))	x	-inf
4.0ms	(expm1.f64 (/.f64 x (hypot.f64 x (*.f64 p 2))))	x	inf

rewrite53.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

460×	`log-prod_binary64`
257×	`pow2_binary64`
182×	`expm1-udef_binary64`
182×	`log1p-udef_binary64`
180×	`pow1/3_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	36
1	210	36
2	2469	36

Stop Event

1×	node limit

Counts

3 → 101

simplify42.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

868×	`times-frac_binary64`
426×	`fma-def_binary64`
416×	`associate-/l*_binary64`
396×	`associate-/r*_binary64`
321×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	149	1855
1	481	1773
2	1608	1662

Stop Event

1×	node limit

Counts

173 → 186

prune189.0ms (2.9%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	253	0	253
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	253	5	258

Error

5.1b

Counts

258 → 5

Alt Table

Status	Error	Program
▶	13.0b	(sqrt.f64 (+.f64 (log.f64 (sqrt.f64 (exp.f64 (fma.f64 1/2 (/.f64 x (hypot.f64 x (.f64 p 2))) 1/2)))) (log.f64 (sqrt.f64 (exp.f64 (fma.f64 1/2 (/.f64 x (hypot.f64 x (.f64 p 2))) 1/2))))))
	55.2b	(sqrt.f64 (-.f64 (/.f64 (pow.f64 p 2) (pow.f64 x 2)) (*.f64 3 (/.f64 (pow.f64 p 4) (pow.f64 x 4)))))
✓	12.6b	(sqrt.f64 (fma.f64 1/2 (log1p.f64 (expm1.f64 (/.f64 x (hypot.f64 x (*.f64 p 2))))) 1/2))
✓	12.6b	(sqrt.f64 (expm1.f64 (log1p.f64 (fma.f64 1/2 (/.f64 x (hypot.f64 x (*.f64 p 2))) 1/2))))
	51.6b	(sqrt.f64 (*.f64 (/.f64 p x) (/.f64 p x)))

Compiler

Compiled 5343 to 3204 computations (40% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (+.f64 (log.f64 (sqrt.f64 (exp.f64 (fma.f64 1/2 (/.f64 x (hypot.f64 x (.f64 p 2))) 1/2)))) (log.f64 (sqrt.f64 (exp.f64 (fma.f64 1/2 (/.f64 x (hypot.f64 x (.f64 p 2))) 1/2))))))
	0.0b	(/.f64 x (hypot.f64 x (*.f64 p 2)))
	0.6b	(fma.f64 1/2 (/.f64 x (hypot.f64 x (*.f64 p 2))) 1/2)
✓	1.5b	(log.f64 (sqrt.f64 (exp.f64 (fma.f64 1/2 (/.f64 x (hypot.f64 x (*.f64 p 2))) 1/2))))

series150.0ms (2.3%)

Counts

2 → 48

Calls

12 calls:

33.0ms	(sqrt.f64 (+.f64 (log.f64 (sqrt.f64 (exp.f64 (fma.f64 1/2 (/.f64 x (hypot.f64 x (.f64 p 2))) 1/2)))) (log.f64 (sqrt.f64 (exp.f64 (fma.f64 1/2 (/.f64 x (hypot.f64 x (.f64 p 2))) 1/2))))))	x	inf
30.0ms	(sqrt.f64 (+.f64 (log.f64 (sqrt.f64 (exp.f64 (fma.f64 1/2 (/.f64 x (hypot.f64 x (.f64 p 2))) 1/2)))) (log.f64 (sqrt.f64 (exp.f64 (fma.f64 1/2 (/.f64 x (hypot.f64 x (.f64 p 2))) 1/2))))))	p	0
14.0ms	(sqrt.f64 (+.f64 (log.f64 (sqrt.f64 (exp.f64 (fma.f64 1/2 (/.f64 x (hypot.f64 x (.f64 p 2))) 1/2)))) (log.f64 (sqrt.f64 (exp.f64 (fma.f64 1/2 (/.f64 x (hypot.f64 x (.f64 p 2))) 1/2))))))	x	-inf
12.0ms	(sqrt.f64 (+.f64 (log.f64 (sqrt.f64 (exp.f64 (fma.f64 1/2 (/.f64 x (hypot.f64 x (.f64 p 2))) 1/2)))) (log.f64 (sqrt.f64 (exp.f64 (fma.f64 1/2 (/.f64 x (hypot.f64 x (.f64 p 2))) 1/2))))))	p	-inf
12.0ms	(log.f64 (sqrt.f64 (exp.f64 (fma.f64 1/2 (/.f64 x (hypot.f64 x (*.f64 p 2))) 1/2))))	x	inf

rewrite50.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

301×	`prod-diff_binary64`
205×	`expm1-udef_binary64`
205×	`log1p-udef_binary64`
186×	`log-pow_binary64`
156×	`fma-def_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	36
1	290	11
2	3360	11

Stop Event

1×	node limit

Counts

2 → 111

simplify81.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

316×	`times-frac_binary64`
285×	`fma-def_binary64`
257×	`fma-neg_binary64`
216×	`associate-/r*_binary64`
204×	`*-commutative_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	315	4069
1	1095	3421
2	4793	3421

Stop Event

1×	node limit

Counts

159 → 173

prune423.0ms (6.6%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	471	2	473
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	471	7	478

Error

2.6b

Counts

478 → 7

Alt Table

Status	Error	Program
	53.4b	(/.f64 (neg.f64 (sqrt.f64 1/2)) (/.f64 (/.f64 x (sqrt.f64 2)) p))
✓	12.6b	(sqrt.f64 (fma.f64 1/2 (log1p.f64 (expm1.f64 (/.f64 x (hypot.f64 x (*.f64 p 2))))) 1/2))
✓	13.0b	(sqrt.f64 (+.f64 (log.f64 (sqrt.f64 (exp.f64 (fma.f64 1/2 (/.f64 x (hypot.f64 x (.f64 p 2))) 1/2)))) (log.f64 (sqrt.f64 (exp.f64 (fma.f64 1/2 (/.f64 x (hypot.f64 x (.f64 p 2))) 1/2))))))
	55.2b	(sqrt.f64 (-.f64 (/.f64 (pow.f64 p 2) (pow.f64 x 2)) (*.f64 3 (/.f64 (pow.f64 p 4) (pow.f64 x 4)))))
	54.6b	(-.f64 (.f64 (.f64 3/4 (/.f64 (sqrt.f64 2) (sqrt.f64 1/2))) (/.f64 (pow.f64 p 3) (pow.f64 x 3))) (.f64 (/.f64 (sqrt.f64 1/2) x) (.f64 p (sqrt.f64 2))))
✓	12.6b	(sqrt.f64 (expm1.f64 (log1p.f64 (fma.f64 1/2 (/.f64 x (hypot.f64 x (*.f64 p 2))) 1/2))))
	51.6b	(sqrt.f64 (*.f64 (/.f64 p x) (/.f64 p x)))

Compiler

Compiled 16117 to 12175 computations (24.5% saved)

regimes1.3s (20.4%)

Accuracy

Total 2.7b remaining (47.6%)

Threshold costs 0b (0%)

Counts

168 → 2

Compiler

Compiled 20464 to 16517 computations (19.3% saved)

bsearch5.0ms (0.1%)

Algorithm

1×	left-value

Calls

1 calls:

0.0ms

(/.f64 x (sqrt.f64 (+.f64 (*.f64 (*.f64 4 p) p) (*.f64 x x))))

Steps

Iters	Point		Range
-0.9999999999534861	∈ [	-0.9999999999534861	,	-4.4322780072727704e-7	]

Compiler

Compiled 14 to 9 computations (35.7% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`
1×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	59
1	30	59

Stop Event

1×

saturated

end123.0ms (1.9%)

Stop Event

1×

fuel

Compiler

Compiled 209 to 154 computations (26.3% saved)

Details

analyze1.2s (17.9%)

sample2.0s (31.6%)

preprocess20.0ms (0.3%)

simplify7.0ms (0.1%)

prune7.0ms (0.1%)

localize9.0ms (0.1%)

series55.0ms (0.9%)

rewrite52.0ms (0.8%)

simplify50.0ms (0.8%)

prune204.0ms (3.2%)

localize10.0ms (0.1%)

series64.0ms (1%)

rewrite53.0ms (0.8%)

simplify48.0ms (0.7%)

prune155.0ms (2.4%)

localize10.0ms (0.2%)

series53.0ms (0.8%)

rewrite53.0ms (0.8%)

simplify42.0ms (0.7%)

prune189.0ms (2.9%)

localize12.0ms (0.2%)

series150.0ms (2.3%)

rewrite50.0ms (0.8%)

simplify81.0ms (1.3%)

prune423.0ms (6.6%)

regimes1.3s (20.4%)

bsearch5.0ms (0.1%)

simplify2.0ms (0%)

end123.0ms (1.9%)

Profiling