Details

analyze80.0ms (3.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	37.5%	62.5%	0
0%	37.5%	62.5%	1
0%	18.7%	81.3%	2
0%	9.4%	90.6%	3
0%	9.4%	90.6%	4
0%	7%	93%	5
1.2%	4.7%	94.1%	6
1.2%	3.5%	95.3%	7
1.8%	2.6%	95.6%	8
2%	1.9%	96%	9
2.4%	1.3%	96.3%	10
2.6%	1%	96.5%	11
2.7%	0.7%	96.6%	12
2.8%	0.5%	96.7%	13
2.9%	0.3%	96.7%	14

Compiler

Compiled 26 to 15 computations (42.3% saved)

sample30.0ms (1.2%)

Algorithm

1×

intervals

Results

12.0ms	256×	body	128	valid
7.0ms	256×	pre	128	true
0.0ms	20×	pre	128	false

Compiler

Compiled 43 to 25 computations (41.9% saved)

simplify47.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

704×	`fma-def_binary64`
643×	`fma-neg_binary64`
603×	`associate-/r*_binary64`
566×	`associate-l_binary64`
362×	`distribute-rgt-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	9	20
1	26	17
2	69	15
3	194	15
4	464	15
5	1521	15
6	4781	15
7	5160	15

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

12.5b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	12.5b	(sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 b (*.f64 a a)) -1)))

Compiler

Compiled 49 to 29 computations (40.8% saved)

localize7.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 b (*.f64 a a)) -1)))
✓	12.8b	(/.f64 b (*.f64 a a))

series42.0ms (1.6%)

Counts

2 → 48

Calls

2 calls:

28.0ms	(/.f64 b (*.f64 a a))
14.0ms	(sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 b (*.f64 a a)) -1)))

rewrite7.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-sqr-sqrt_binary64`
7×	`sqrt-prod_binary64`
7×	`add-cbrt-cube_binary64`
7×	`add-exp-log_binary64`
6×	`*-un-lft-identity_binary64`

Counts

2 → 44

Calls

2 calls:

4.0ms	(/.f64 b (*.f64 a a))
2.0ms	(sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 b (*.f64 a a)) -1)))

simplify85.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

553×	`div-sub_binary64`
385×	`associate-/l*_binary64`
361×	`associate-/l/_binary64`
322×	`*-commutative_binary64`
270×	`fma-def_binary64`

Counts

92 → 53

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	80	1190
1	131	1118
2	258	1118
3	623	1118
4	1939	1118
5	2527	1118
6	4267	1118
7	5200	1118

prune31.0ms (1.2%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	52	1	53
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	53	1	54

Error

0.0b

Counts

54 → 1

Alt Table

Status	Error	Program
▶	0.0b	(sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 (/.f64 b a) a) -1)))

Compiler

Compiled 868 to 419 computations (51.7% saved)

localize7.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 (/.f64 b a) a) -1)))
✓	0.2b	(/.f64 (/.f64 b a) a)

series42.0ms (1.6%)

Counts

2 → 48

Calls

2 calls:

28.0ms	(/.f64 (/.f64 b a) a)
14.0ms	(sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 (/.f64 b a) a) -1)))

rewrite12.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

75×	`times-frac_binary64`
50×	`add-sqr-sqrt_binary64`
46×	`*-un-lft-identity_binary64`
46×	`add-cube-cbrt_binary64`
13×	`associate-/l*_binary64`

Counts

2 → 93

Calls

2 calls:

4.0ms	(/.f64 (/.f64 b a) a)
1.0ms	(sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 (/.f64 b a) a) -1)))

simplify148.0ms (5.7%)

Algorithm

1×	egg-herbie

Rules

360×	`distribute-rgt-in_binary64`
345×	`fma-neg_binary64`
327×	`associate-/l/_binary64`
305×	`distribute-lft-in_binary64`
298×	`fma-def_binary64`

Counts

141 → 146

Iterations

Useful iterations: 6 (0.0ms)

Iter	Nodes	Cost
0	174	2231
1	333	2103
2	605	2031
3	1372	2007
4	1707	2002
5	2563	1952
6	4418	1922
7	4987	1922
8	4849	1922

prune77.0ms (3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	144	2	146
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	144	3	147

Error

0.0b

Counts

147 → 3

Alt Table

Status	Error	Program
✓	0.0b	(sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 (/.f64 b a) a) -1)))
▶	0.0b	(log1p.f64 (expm1.f64 (sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 (/.f64 b a) a) -1)))))
	0.0b	(expm1.f64 (log1p.f64 (sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 (/.f64 b a) a) -1)))))

Compiler

Compiled 2729 to 1217 computations (55.4% saved)

localize10.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 (/.f64 b a) a) -1)))
✓	0.0b	(log1p.f64 (expm1.f64 (sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 (/.f64 b a) a) -1)))))
	0.2b	(/.f64 (/.f64 b a) a)
✓	1.0b	(expm1.f64 (sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 (/.f64 b a) a) -1))))

series35.0ms (1.4%)

Counts

2 → 48

Calls

2 calls:

22.0ms	(expm1.f64 (sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 (/.f64 b a) a) -1))))
13.0ms	(log1p.f64 (expm1.f64 (sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 (/.f64 b a) a) -1)))))

rewrite1.0ms (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 (sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 (/.f64 b a) a) -1))))
0.0ms	(log1p.f64 (expm1.f64 (sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 (/.f64 b a) a) -1)))))

simplify106.0ms (4.1%)

Algorithm

1×	egg-herbie

Rules

763×	`unsub-neg_binary64`
458×	`unswap-sqr_binary64`
354×	`distribute-rgt-in_binary64`
341×	`associate-l_binary64`
303×	`associate-/l/_binary64`

Counts

70 → 40

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	39	1230
1	46	1164
2	86	1164
3	158	1164
4	462	1164
5	2017	1164
6	4012	1164
7	5313	1164

prune157.0ms (6.1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	184	2	186
Fresh	1	0	1
Picked	1	0	1
Done	0	1	1
Total	186	3	189

Error

Counts

189 → 3

Alt Table

Status	Error	Program
✓	0.0b	(sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 (/.f64 b a) a) -1)))
	0.0b	(expm1.f64 (log1p.f64 (log1p.f64 (expm1.f64 (sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 (/.f64 b a) a) -1)))))))
▶	0.0b	(log1p.f64 (*.f64 (sqrt.f64 (expm1.f64 (sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 (/.f64 b a) a) -1))))) (sqrt.f64 (expm1.f64 (sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 (/.f64 b a) a) -1)))))))

Compiler

Compiled 3781 to 1927 computations (49% saved)

localize12.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(log1p.f64 (*.f64 (sqrt.f64 (expm1.f64 (sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 (/.f64 b a) a) -1))))) (sqrt.f64 (expm1.f64 (sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 (/.f64 b a) a) -1)))))))
	0.2b	(/.f64 (/.f64 b a) a)
	1.0b	(expm1.f64 (sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 (/.f64 b a) a) -1))))
✓	1.0b	(*.f64 (sqrt.f64 (expm1.f64 (sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 (/.f64 b a) a) -1))))) (sqrt.f64 (expm1.f64 (sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 (/.f64 b a) a) -1))))))

series36.0ms (1.4%)

Counts

2 → 48

Calls

2 calls:

23.0ms

(*.f64 (sqrt.f64 (expm1.f64 (sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 (/.f64 b a) a) -1))))) (sqrt.f64 (expm1.f64 (sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 (/.f64 b a) a) -1))))))

13.0ms

(log1p.f64 (*.f64 (sqrt.f64 (expm1.f64 (sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 (/.f64 b a) a) -1))))) (sqrt.f64 (expm1.f64 (sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 (/.f64 b a) a) -1)))))))

rewrite13.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`add-sqr-sqrt_binary64`
18×	`sqrt-prod_binary64`
17×	`pow1_binary64`
10×	`*-un-lft-identity_binary64`
10×	`add-cube-cbrt_binary64`

Counts

2 → 64

Calls

2 calls:

5.0ms

(*.f64 (sqrt.f64 (expm1.f64 (sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 (/.f64 b a) a) -1))))) (sqrt.f64 (expm1.f64 (sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 (/.f64 b a) a) -1))))))

0.0ms

(log1p.f64 (*.f64 (sqrt.f64 (expm1.f64 (sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 (/.f64 b a) a) -1))))) (sqrt.f64 (expm1.f64 (sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 (/.f64 b a) a) -1)))))))

simplify136.0ms (5.3%)

Algorithm

1×	egg-herbie

Rules

652×	`difference-of-squares_binary64`
464×	`unswap-sqr_binary64`
316×	`log-prod_binary64`
300×	`distribute-rgt-in_binary64`
271×	`distribute-lft-in_binary64`

Counts

112 → 83

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	71	2392
1	99	2179
2	242	2095
3	651	1969
4	1829	1969
5	3161	1969
6	4731	1969
7	4752	1969

prune339.0ms (13.1%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	347	0	347
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	347	3	350

Error

Counts

350 → 3

Alt Table

Status	Error	Program
✓	0.0b	(sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 (/.f64 b a) a) -1)))
	0.0b	(expm1.f64 (log1p.f64 (log1p.f64 (expm1.f64 (sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 (/.f64 b a) a) -1)))))))
✓	0.0b	(log1p.f64 (*.f64 (sqrt.f64 (expm1.f64 (sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 (/.f64 b a) a) -1))))) (sqrt.f64 (expm1.f64 (sqrt.f64 (fabs.f64 (fma.f64 b (/.f64 (/.f64 b a) a) -1)))))))

Compiler

Compiled 11606 to 6061 computations (47.8% saved)

regimes131.0ms (5.1%)

Accuracy

Total 0.0b remaining (80.3%)

Threshold costs 0.0b (80.3%)

Counts

21 → 1

Compiler

Compiled 2696 to 1865 computations (30.8% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	23
1	13	23

end1.0ms (0%)

Compiler: Compiled 16 to 12 computations (25% saved)

sample984.0ms (38.1%)

Algorithm

1×

intervals

Results

381.0ms	8000×	body	128	valid
198.0ms	8000×	pre	128	true
9.0ms	374×	pre	128	false

Compiler

Compiled 100 to 67 computations (33% saved)

Details

analyze80.0ms (3.1%)

sample30.0ms (1.2%)

simplify47.0ms (1.8%)

prune3.0ms (0.1%)

localize7.0ms (0.3%)

series42.0ms (1.6%)

rewrite7.0ms (0.3%)

simplify85.0ms (3.3%)

prune31.0ms (1.2%)

localize7.0ms (0.3%)

series42.0ms (1.6%)

rewrite12.0ms (0.5%)

simplify148.0ms (5.7%)

prune77.0ms (3%)

localize10.0ms (0.4%)

series35.0ms (1.4%)

rewrite1.0ms (0.1%)

simplify106.0ms (4.1%)

prune157.0ms (6.1%)

localize12.0ms (0.5%)

series36.0ms (1.4%)

rewrite13.0ms (0.5%)

simplify136.0ms (5.3%)

prune339.0ms (13.1%)

regimes131.0ms (5.1%)

simplify2.0ms (0.1%)

end1.0ms (0%)

sample984.0ms (38.1%)

Profiling