Details

analyze6.0ms (0.3%)

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%	50.1%	13
49.9%	0%	50.1%	14

Compiler

Compiled 21 to 16 computations (23.8% saved)

sample1.1s (49.6%)

Results

1.0s	8256×	body	128	valid
0.0ms	3×	body	128	invalid

Compiler

Compiled 62 to 47 computations (24.2% saved)

simplify76.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

750×	`div-sub_binary64`
748×	`fma-neg_binary64`
599×	`fma-def_binary64`
502×	`associate-/l*_binary64`
423×	`distribute-rgt-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	15	29
1	37	29
2	82	27
3	201	27
4	526	27
5	991	25
6	1614	25
7	3273	25
8	3653	25
9	4694	25
10	4942	25

prune4.0ms (0.2%)

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

0.0b

Counts

3 → 2

Alt Table

Status	Error	Program
	0.0b	(.f64 (.f64 (/.f64 (sqrt.f64 2) 4) (sqrt.f64 (-.f64 1 (.f64 3 (.f64 v v))))) (-.f64 1 (*.f64 v v)))
▶	0.0b	(.f64 (sqrt.f64 2) (.f64 (sqrt.f64 (fma.f64 v (.f64 v -3) 1)) (.f64 -1/4 (fma.f64 v v -1))))

Compiler

Compiled 113 to 86 computations (23.9% saved)

localize10.0ms (0.4%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (fma.f64 v (*.f64 v -3) 1))
✓	0.0b	(.f64 (sqrt.f64 (fma.f64 v (.f64 v -3) 1)) (*.f64 -1/4 (fma.f64 v v -1)))
✓	0.0b	(.f64 (sqrt.f64 2) (.f64 (sqrt.f64 (fma.f64 v (.f64 v -3) 1)) (.f64 -1/4 (fma.f64 v v -1))))

series28.0ms (1.2%)

Counts

3 → 36

Calls

3 calls:

14.0ms

(*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 (fma.f64 v (*.f64 v -3) 1)) (*.f64 -1/4 (fma.f64 v v -1))))

9.0ms

(*.f64 (sqrt.f64 (fma.f64 v (*.f64 v -3) 1)) (*.f64 -1/4 (fma.f64 v v -1)))

4.0ms

(sqrt.f64 (fma.f64 v (*.f64 v -3) 1))

rewrite70.0ms (3%)

Algorithm

2×	batch-egg-rewrite

Rules

629×	`log-prod_binary64`
233×	`expm1-udef_binary64`
233×	`log1p-udef_binary64`
202×	`log-pow_binary64`
134×	`add-sqr-sqrt_binary64`

Counts

3 → 68

Calls

3 calls:

68.0ms

(sqrt.f64 (fma.f64 v (*.f64 v -3) 1))

68.0ms

(*.f64 (sqrt.f64 (fma.f64 v (*.f64 v -3) 1)) (*.f64 -1/4 (fma.f64 v v -1)))

68.0ms

(*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 (fma.f64 v (*.f64 v -3) 1)) (*.f64 -1/4 (fma.f64 v v -1))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	55
1	292	53
2	3049	53
3	4979	53
0	0	0
1	0	0

simplify68.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

716×	`fma-def_binary64`
690×	`fma-neg_binary64`
569×	`cancel-sign-sub-inv_binary64`
444×	`times-frac_binary64`
381×	`associate-/r*_binary64`

Counts

104 → 132

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	133	1310
1	444	1257
2	1628	1102
3	4372	1098
4	5183	1098

prune156.0ms (6.7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	130	2	132
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	131	3	134

Error

Counts

134 → 3

Alt Table

Status	Error	Program
▶	0.0b	(expm1.f64 (log1p.f64 (.f64 (.f64 -1/4 (fma.f64 v v -1)) (sqrt.f64 (.f64 2 (fma.f64 v (.f64 v -3) 1))))))
✓	0.0b	(.f64 (sqrt.f64 2) (.f64 (sqrt.f64 (fma.f64 v (.f64 v -3) 1)) (.f64 -1/4 (fma.f64 v v -1))))
	0.2b	(.f64 (sqrt.f64 2) (fma.f64 (.f64 v v) -5/8 1/4))

Compiler

Compiled 3527 to 2933 computations (16.8% saved)

localize12.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (.f64 2 (fma.f64 v (.f64 v -3) 1)))
✓	0.0b	(.f64 (.f64 -1/4 (fma.f64 v v -1)) (sqrt.f64 (.f64 2 (fma.f64 v (.f64 v -3) 1))))
✓	0.0b	(log1p.f64 (.f64 (.f64 -1/4 (fma.f64 v v -1)) (sqrt.f64 (.f64 2 (fma.f64 v (.f64 v -3) 1)))))
✓	0.0b	(expm1.f64 (log1p.f64 (.f64 (.f64 -1/4 (fma.f64 v v -1)) (sqrt.f64 (.f64 2 (fma.f64 v (.f64 v -3) 1))))))

series55.0ms (2.4%)

Counts

4 → 48

Calls

4 calls:

21.0ms	(log1p.f64 (.f64 (.f64 -1/4 (fma.f64 v v -1)) (sqrt.f64 (.f64 2 (fma.f64 v (.f64 v -3) 1)))))
12.0ms	(.f64 (.f64 -1/4 (fma.f64 v v -1)) (sqrt.f64 (.f64 2 (fma.f64 v (.f64 v -3) 1))))
12.0ms	(expm1.f64 (log1p.f64 (.f64 (.f64 -1/4 (fma.f64 v v -1)) (sqrt.f64 (.f64 2 (fma.f64 v (.f64 v -3) 1))))))
9.0ms	(sqrt.f64 (.f64 2 (fma.f64 v (.f64 v -3) 1)))

rewrite73.0ms (3.2%)

Algorithm

2×	batch-egg-rewrite

Rules

616×	`log-prod_binary64`
336×	`prod-diff_binary64`
234×	`expm1-udef_binary64`
234×	`log1p-udef_binary64`
202×	`log-pow_binary64`

Counts

4 → 117

Calls

4 calls:

70.0ms	(sqrt.f64 (.f64 2 (fma.f64 v (.f64 v -3) 1)))
70.0ms	(.f64 (.f64 -1/4 (fma.f64 v v -1)) (sqrt.f64 (.f64 2 (fma.f64 v (.f64 v -3) 1))))
70.0ms	(log1p.f64 (.f64 (.f64 -1/4 (fma.f64 v v -1)) (sqrt.f64 (.f64 2 (fma.f64 v (.f64 v -3) 1)))))
70.0ms	(expm1.f64 (log1p.f64 (.f64 (.f64 -1/4 (fma.f64 v v -1)) (sqrt.f64 (.f64 2 (fma.f64 v (.f64 v -3) 1))))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	84
1	292	84
2	3036	84
3	5465	84
0	0	0
1	0	0

simplify85.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

825×	`times-frac_binary64`
823×	`fma-def_binary64`
728×	`fma-neg_binary64`
266×	`sub-neg_binary64`
106×	`associate-r_binary64`

Counts

165 → 161

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	174	2396
1	585	2196
2	2219	2109
3	4986	2109
4	5388	2109

prune147.0ms (6.3%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	161	0	161
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	161	3	164

Error

Counts

164 → 3

Alt Table

Status	Error	Program
✓	0.0b	(expm1.f64 (log1p.f64 (.f64 (.f64 -1/4 (fma.f64 v v -1)) (sqrt.f64 (.f64 2 (fma.f64 v (.f64 v -3) 1))))))
✓	0.0b	(.f64 (sqrt.f64 2) (.f64 (sqrt.f64 (fma.f64 v (.f64 v -3) 1)) (.f64 -1/4 (fma.f64 v v -1))))
▶	0.2b	(.f64 (sqrt.f64 2) (fma.f64 (.f64 v v) -5/8 1/4))

Compiler

Compiled 4906 to 4105 computations (16.3% saved)

localize5.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 (sqrt.f64 2) (fma.f64 (.f64 v v) -5/8 1/4))

series5.0ms (0.2%)

Counts

1 → 12

Calls

1 calls:

5.0ms

(*.f64 (sqrt.f64 2) (fma.f64 (*.f64 v v) -5/8 1/4))

rewrite41.0ms (1.8%)

Algorithm

2×	batch-egg-rewrite

Rules

682×	`log1p-expm1-u_binary64`
682×	`expm1-log1p-u_binary64`
326×	`log-prod_binary64`
143×	`expm1-udef_binary64`
143×	`log1p-udef_binary64`

Counts

1 → 22

Calls

1 calls:

40.0ms

(*.f64 (sqrt.f64 2) (fma.f64 (*.f64 v v) -5/8 1/4))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	181	13
2	1789	13
3	5154	13
0	0	0
1	0	0

simplify149.0ms (6.4%)

Algorithm

1×	egg-herbie

Rules

1403×	`fma-def_binary64`
1077×	`cube-prod_binary64`
943×	`fabs-mul_binary64`
684×	`unswap-sqr_binary64`
514×	`distribute-rgt-neg-in_binary64`

Counts

34 → 27

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	13	210
1	31	165
2	72	165
3	179	147
4	487	147
5	798	147
6	1205	147
7	1711	147
8	2672	147
9	4044	147
10	3953	147
11	4156	147
12	3405	147
13	3503	147
14	4208	147
15	4599	147
16	4794	147

prune26.0ms (1.1%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	27	0	27
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	27	3	30

Error

Counts

30 → 3

Alt Table

Status	Error	Program
✓	0.0b	(expm1.f64 (log1p.f64 (.f64 (.f64 -1/4 (fma.f64 v v -1)) (sqrt.f64 (.f64 2 (fma.f64 v (.f64 v -3) 1))))))
✓	0.0b	(.f64 (sqrt.f64 2) (.f64 (sqrt.f64 (fma.f64 v (.f64 v -3) 1)) (.f64 -1/4 (fma.f64 v v -1))))
✓	0.2b	(.f64 (sqrt.f64 2) (fma.f64 (.f64 v v) -5/8 1/4))

Compiler

Compiled 395 to 303 computations (23.3% saved)

regimes86.0ms (3.7%)

Accuracy

Total 0.0b remaining (50%)

Threshold costs 0.0b (50%)

Counts

30 → 1

Compiler

Compiled 1660 to 1350 computations (18.7% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	25
1	21	25
2	20	25

end66.0ms (2.9%)

Compiler: Compiled 83 to 65 computations (21.7% saved)

Details

analyze6.0ms (0.3%)

sample1.1s (49.6%)

simplify76.0ms (3.3%)

prune4.0ms (0.2%)

localize10.0ms (0.4%)

series28.0ms (1.2%)

rewrite70.0ms (3%)

simplify68.0ms (2.9%)

prune156.0ms (6.7%)

localize12.0ms (0.5%)

series55.0ms (2.4%)

rewrite73.0ms (3.2%)

simplify85.0ms (3.7%)

prune147.0ms (6.3%)

localize5.0ms (0.2%)

series5.0ms (0.2%)

rewrite41.0ms (1.8%)

simplify149.0ms (6.4%)

prune26.0ms (1.1%)

regimes86.0ms (3.7%)

simplify2.0ms (0.1%)

end66.0ms (2.9%)

Profiling