Details

analyze11.0ms (0.5%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	50%	50%	3
25%	25%	50%	4
37.5%	12.5%	50%	5
43.7%	6.2%	50%	6
46.9%	3.1%	50%	7
48.4%	1.6%	50%	8
49.2%	0.8%	50%	9
49.6%	0.4%	50%	10
49.8%	0.2%	50%	11
49.9%	0.1%	50%	12
49.9%	0%	50%	13
49.9%	0%	50%	14

Compiler

Compiled 13 to 11 computations (15.4% saved)

sample1.1s (47.7%)

Results

1.1s

8256×

body

128

valid

Compiler

Compiled 38 to 32 computations (15.8% saved)

simplify26.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

396×	`fma-neg_binary64`
375×	`fma-def_binary64`
260×	`div-sub_binary64`
121×	`times-frac_binary64`
111×	`associate-/l*_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	17
1	19	17
2	25	17
3	35	17
4	58	17
5	82	17
6	117	17
7	189	17
8	356	17
9	577	17
10	789	17
11	1134	17
12	1524	17
13	1940	17
14	2181	17

Stop Event

1×

saturated

Counts

1 → 2

prune2.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

0.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.0b	(*.f64 2 (atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))))

Compiler

Compiled 47 to 39 computations (17% saved)

localize7.0ms (0.3%)

Local error

Found 3 expressions with local error:

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

series10.0ms (0.4%)

Counts

3 → 24

Calls

3 calls:

4.0ms	(sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))
3.0ms	(atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))
2.0ms	(/.f64 (-.f64 1 x) (+.f64 1 x))

rewrite79.0ms (3.4%)

Algorithm

1×	batch-egg-rewrite

Rules

913×	`log1p-expm1-u_binary64`
913×	`expm1-log1p-u_binary64`
311×	`prod-diff_binary64`
161×	`egg-rr`
85×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	36
1	177	36
2	2408	36

Stop Event

1×	node limit

Counts

3 → 161

Calls

3 calls:

73.0ms	(atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))
73.0ms	(sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))
73.0ms	(/.f64 (-.f64 1 x) (+.f64 1 x))

simplify32.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

692×	`fma-def_binary64`
444×	`cancel-sign-sub-inv_binary64`
314×	`fma-neg_binary64`
262×	`associate-/l/_binary64`
194×	`sub-neg_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	61	494
1	189	468
2	609	456
3	2374	394

Stop Event

1×	node limit

Counts

185 → 187

prune185.0ms (7.9%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	184	3	187
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	185	3	188

Error

Counts

188 → 3

Alt Table

Status	Error	Program
	0.0b	(*.f64 2 (-.f64 (exp.f64 (log1p.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))))) 1))
▶	0.0b	(.f64 2 (atan.f64 (exp.f64 (.f64 1/2 (-.f64 (log1p.f64 (neg.f64 x)) (log1p.f64 x))))))
	0.0b	(*.f64 2 (atan.f64 (cbrt.f64 (pow.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 3/2))))

Compiler

Compiled 6065 to 4084 computations (32.7% saved)

localize9.0ms (0.4%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (log1p.f64 (neg.f64 x)) (log1p.f64 x))
✓	0.0b	(atan.f64 (exp.f64 (*.f64 1/2 (-.f64 (log1p.f64 (neg.f64 x)) (log1p.f64 x)))))

series5.0ms (0.2%)

Counts

2 → 16

Calls

2 calls:

3.0ms	(-.f64 (log1p.f64 (neg.f64 x)) (log1p.f64 x))
2.0ms	(atan.f64 (exp.f64 (*.f64 1/2 (-.f64 (log1p.f64 (neg.f64 x)) (log1p.f64 x)))))

rewrite42.0ms (1.8%)

Algorithm

1×	batch-egg-rewrite

Rules

793×	`expm1-log1p-u_binary64`
791×	`log1p-expm1-u_binary64`
391×	`prod-diff_binary64`
103×	`add-sqr-sqrt_binary64`
96×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	27
1	207	23
2	2706	23

Stop Event

1×	node limit

Counts

2 → 67

Calls

2 calls:

41.0ms	(-.f64 (log1p.f64 (neg.f64 x)) (log1p.f64 x))
41.0ms	(atan.f64 (exp.f64 (*.f64 1/2 (-.f64 (log1p.f64 (neg.f64 x)) (log1p.f64 x)))))

simplify31.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

622×	`fma-neg_binary64`
452×	`sub-neg_binary64`
326×	`cancel-sign-sub-inv_binary64`
194×	`associate-+l-_binary64`
189×	`fma-def_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	55	254
1	161	248
2	473	240
3	1609	238
4	4252	238

Stop Event

1×	node limit

Counts

83 → 92

prune67.0ms (2.9%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	92	0	92
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	92	3	95

Error

Counts

95 → 3

Alt Table

Status	Error	Program
	0.0b	(*.f64 2 (-.f64 (exp.f64 (log1p.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))))) 1))
✓	0.0b	(.f64 2 (atan.f64 (exp.f64 (.f64 1/2 (-.f64 (log1p.f64 (neg.f64 x)) (log1p.f64 x))))))
▶	0.0b	(*.f64 2 (atan.f64 (cbrt.f64 (pow.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 3/2))))

Compiler

Compiled 1788 to 1151 computations (35.6% saved)

localize9.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(pow.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 3/2)
✓	0.0b	(atan.f64 (cbrt.f64 (pow.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 3/2)))
	0.0b	(/.f64 (-.f64 1 x) (+.f64 1 x))
✓	0.0b	(cbrt.f64 (pow.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 3/2))

series9.0ms (0.4%)

Counts

3 → 36

Calls

3 calls:

4.0ms	(cbrt.f64 (pow.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 3/2))
3.0ms	(pow.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 3/2)
2.0ms	(atan.f64 (cbrt.f64 (pow.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 3/2)))

rewrite56.0ms (2.4%)

Algorithm

1×	batch-egg-rewrite

Rules

473×	`log-prod_binary64`
311×	`prod-diff_binary64`
182×	`fma-def_binary64`
178×	`expm1-udef_binary64`
177×	`log1p-udef_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	45
1	221	39
2	2846	39

Stop Event

1×	node limit

Counts

3 → 74

Calls

3 calls:

55.0ms	(pow.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 3/2)
55.0ms	(atan.f64 (cbrt.f64 (pow.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 3/2)))
55.0ms	(cbrt.f64 (pow.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 3/2))

simplify32.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

693×	`fma-def_binary64`
477×	`cancel-sign-sub-inv_binary64`
309×	`fma-neg_binary64`
207×	`times-frac_binary64`
197×	`sub-neg_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	67	735
1	198	703
2	644	671
3	2561	647

Stop Event

1×	node limit

Counts

110 → 100

prune210.0ms (9%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	225	1	226
Fresh	1	0	1
Picked	0	1	1
Done	0	1	1
Total	226	3	229

Error

Counts

229 → 3

Alt Table

Status	Error	Program
✓	0.0b	(.f64 2 (atan.f64 (exp.f64 (.f64 1/2 (-.f64 (log1p.f64 (neg.f64 x)) (log1p.f64 x))))))
✓	0.0b	(*.f64 2 (atan.f64 (cbrt.f64 (pow.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 3/2))))
▶	0.4b	(*.f64 2 (atan.f64 (cbrt.f64 (fma.f64 x (fma.f64 x 9/2 -3) 1))))

Compiler

Compiled 7075 to 4985 computations (29.5% saved)

localize7.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(atan.f64 (cbrt.f64 (fma.f64 x (fma.f64 x 9/2 -3) 1)))
✓	0.0b	(cbrt.f64 (fma.f64 x (fma.f64 x 9/2 -3) 1))

series7.0ms (0.3%)

Counts

2 → 24

Calls

2 calls:

5.0ms	(cbrt.f64 (fma.f64 x (fma.f64 x 9/2 -3) 1))
2.0ms	(atan.f64 (cbrt.f64 (fma.f64 x (fma.f64 x 9/2 -3) 1)))

rewrite38.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

686×	`log1p-expm1-u_binary64`
686×	`expm1-log1p-u_binary64`
313×	`log-prod_binary64`
143×	`expm1-udef_binary64`
143×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	24
1	173	24
2	1831	24

Stop Event

1×	node limit

Counts

2 → 45

Calls

2 calls:

37.0ms	(atan.f64 (cbrt.f64 (fma.f64 x (fma.f64 x 9/2 -3) 1)))
37.0ms	(cbrt.f64 (fma.f64 x (fma.f64 x 9/2 -3) 1))

simplify25.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

710×	`fma-def_binary64`
476×	`times-frac_binary64`
340×	`associate-/l*_binary64`
247×	`associate-/r*_binary64`
225×	`associate-l_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	63	674
1	175	644
2	440	508
3	1442	414

Stop Event

1×	node limit

Counts

69 → 69

prune56.0ms (2.4%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	69	0	69
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	69	3	72

Error

Counts

72 → 3

Alt Table

Status	Error	Program
✓	0.0b	(.f64 2 (atan.f64 (exp.f64 (.f64 1/2 (-.f64 (log1p.f64 (neg.f64 x)) (log1p.f64 x))))))
✓	0.0b	(*.f64 2 (atan.f64 (cbrt.f64 (pow.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 3/2))))
✓	0.4b	(*.f64 2 (atan.f64 (cbrt.f64 (fma.f64 x (fma.f64 x 9/2 -3) 1))))

Compiler

Compiled 1411 to 1203 computations (14.7% saved)

regimes200.0ms (8.6%)

Accuracy

Total 0.0b remaining (51.2%)

Threshold costs 0.0b (51.2%)

Counts

37 → 1

Compiler

Compiled 2799 to 2411 computations (13.9% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	20
1	20	20
2	25	20
3	28	20
4	29	20

Stop Event

1×

saturated

end59.0ms (2.5%)

Compiler: Compiled 65 to 55 computations (15.4% saved)

Details

analyze11.0ms (0.5%)

sample1.1s (47.7%)

simplify26.0ms (1.1%)

prune2.0ms (0.1%)

localize7.0ms (0.3%)

series10.0ms (0.4%)

rewrite79.0ms (3.4%)

simplify32.0ms (1.4%)

prune185.0ms (7.9%)

localize9.0ms (0.4%)

series5.0ms (0.2%)

rewrite42.0ms (1.8%)

simplify31.0ms (1.3%)

prune67.0ms (2.9%)

localize9.0ms (0.4%)

series9.0ms (0.4%)

rewrite56.0ms (2.4%)

simplify32.0ms (1.4%)

prune210.0ms (9%)

localize7.0ms (0.3%)

series7.0ms (0.3%)

rewrite38.0ms (1.6%)

simplify25.0ms (1.1%)

prune56.0ms (2.4%)

regimes200.0ms (8.6%)

simplify2.0ms (0.1%)

end59.0ms (2.5%)

Profiling