Details

analyze313.0ms (7%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	87.4%	12.6%	6
20.3%	59.3%	20.4%	7
21.1%	51.5%	27.4%	8
35.5%	30.4%	34%	9
35.7%	26.1%	38.1%	10
42.8%	15.4%	41.8%	11
42.9%	13.2%	44%	12
46.4%	7.8%	45.8%	13
46.4%	6.6%	47%	14

Compiler

Compiled 32 to 26 computations (18.8% saved)

sample3.2s (70.6%)

Results

1.5s	2131×	body	1024	valid
744.0ms	4355×	body	128	valid
461.0ms	1026×	body	512	valid
223.0ms	210×	body	2048	valid
181.0ms	534×	body	256	valid
71.0ms	434×	body	128	invalid
6.0ms	9×	body	1024	invalid
5.0ms	10×	body	512	invalid
2.0ms	6×	body	256	invalid

Compiler

Compiled 64 to 52 computations (18.8% saved)

preprocess38.0ms (0.9%)

Algorithm

2×	egg-herbie

Rules

232×	`div-sub_binary64`
232×	`fma-def_binary64`
188×	`times-frac_binary64`
184×	`distribute-rgt-neg-in_binary64`
169×	`distribute-lft-neg-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	90
1	103	90
2	299	74
3	959	74
4	3224	74
0	2	2

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 31 to 25 computations (19.4% saved)

simplify21.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

750×	`times-frac_binary64`
534×	`cancel-sign-sub-inv_binary64`
519×	`fma-neg_binary64`
197×	`associate-/l/_binary64`
123×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	20	45
1	57	45
2	159	37
3	510	37
4	1660	37

Stop Event

1×	node limit

Counts

1 → 2

prune5.0ms (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

29.3b

Counts

3 → 2

Alt Table

Status	Error	Program
	30.3b	(*.f64 1/2 (fma.f64 (+.f64 1 (/.f64 1 eps)) (pow.f64 (exp.f64 x) (+.f64 eps -1)) (/.f64 (-.f64 1 (/.f64 1 eps)) (exp.f64 (fma.f64 eps x x)))))
▶	29.3b	(/.f64 (-.f64 (.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (.f64 (-.f64 1 eps) x)))) (.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (neg.f64 (.f64 (+.f64 1 eps) x))))) 2)

Status

Error

Program

30.3b

(*.f64 1/2 (fma.f64 (+.f64 1 (/.f64 1 eps)) (pow.f64 (exp.f64 x) (+.f64 eps -1)) (/.f64 (-.f64 1 (/.f64 1 eps)) (exp.f64 (fma.f64 eps x x)))))

▶

29.3b

(/.f64 (-.f64 (*.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (*.f64 (-.f64 1 eps) x)))) (*.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (neg.f64 (*.f64 (+.f64 1 eps) x))))) 2)

Compiler

Compiled 172 to 133 computations (22.7% saved)

localize18.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(exp.f64 (neg.f64 (*.f64 (-.f64 1 eps) x)))
✓	0.0b	(exp.f64 (neg.f64 (*.f64 (+.f64 1 eps) x)))
✓	0.0b	(*.f64 (+.f64 1 eps) x)
✓	2.4b	(-.f64 (.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (.f64 (-.f64 1 eps) x)))) (.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (neg.f64 (.f64 (+.f64 1 eps) x)))))

series50.0ms (1.1%)

Counts

4 → 92

Calls

24 calls:

12.0ms	(-.f64 (.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (.f64 (-.f64 1 eps) x)))) (.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (neg.f64 (.f64 (+.f64 1 eps) x)))))	eps	0
8.0ms	(-.f64 (.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (.f64 (-.f64 1 eps) x)))) (.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (neg.f64 (.f64 (+.f64 1 eps) x)))))	x	0
6.0ms	(-.f64 (.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (.f64 (-.f64 1 eps) x)))) (.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (neg.f64 (.f64 (+.f64 1 eps) x)))))	x	inf
4.0ms	(-.f64 (.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (.f64 (-.f64 1 eps) x)))) (.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (neg.f64 (.f64 (+.f64 1 eps) x)))))	x	-inf
2.0ms	(-.f64 (.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (.f64 (-.f64 1 eps) x)))) (.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (neg.f64 (.f64 (+.f64 1 eps) x)))))	eps	-inf

rewrite62.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

209×	`add-sqr-sqrt_binary64`
206×	`*-un-lft-identity_binary64`
206×	`pow1_binary64`
194×	`add-log-exp_binary64`
192×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	18	71
1	412	62

Stop Event

1×	node limit

Counts

4 → 124

simplify55.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

542×	`associate--l+_binary64`
346×	`associate--r+_binary64`
297×	`cancel-sign-sub-inv_binary64`
257×	`fma-def_binary64`
188×	`distribute-rgt-out_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	168	2012
1	575	1964
2	2209	1869

Stop Event

1×	node limit

Counts

216 → 179

prune170.0ms (3.8%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	178	1	179
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	179	2	181

Error

0.0b

Counts

181 → 2

Alt Table

Status	Error	Program
▶	20.5b	(/.f64 (-.f64 (fma.f64 (.f64 eps eps) (.f64 x x) (fma.f64 (pow.f64 x 3) 2/3 2)) (fma.f64 x x (.f64 (.f64 eps eps) (*.f64 (pow.f64 x 3) 2/3)))) 2)
✓	29.3b	(/.f64 (-.f64 (.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (.f64 (-.f64 1 eps) x)))) (.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (neg.f64 (.f64 (+.f64 1 eps) x))))) 2)

Status

Error

Program

▶

20.5b

(/.f64 (-.f64 (fma.f64 (*.f64 eps eps) (*.f64 x x) (fma.f64 (pow.f64 x 3) 2/3 2)) (fma.f64 x x (*.f64 (*.f64 eps eps) (*.f64 (pow.f64 x 3) 2/3)))) 2)

✓

29.3b

(/.f64 (-.f64 (*.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (*.f64 (-.f64 1 eps) x)))) (*.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (neg.f64 (*.f64 (+.f64 1 eps) x))))) 2)

Compiler

Compiled 7662 to 5755 computations (24.9% saved)

localize14.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 (pow.f64 x 3) 2/3)
✓	5.9b	(fma.f64 (.f64 eps eps) (.f64 x x) (fma.f64 (pow.f64 x 3) 2/3 2))
✓	6.4b	(-.f64 (fma.f64 (.f64 eps eps) (.f64 x x) (fma.f64 (pow.f64 x 3) 2/3 2)) (fma.f64 x x (.f64 (.f64 eps eps) (*.f64 (pow.f64 x 3) 2/3))))
✓	12.4b	(.f64 (.f64 eps eps) (*.f64 (pow.f64 x 3) 2/3))

series59.0ms (1.3%)

Counts

4 → 84

Calls

21 calls:

6.0ms	(-.f64 (fma.f64 (.f64 eps eps) (.f64 x x) (fma.f64 (pow.f64 x 3) 2/3 2)) (fma.f64 x x (.f64 (.f64 eps eps) (*.f64 (pow.f64 x 3) 2/3))))	eps	-inf
6.0ms	(-.f64 (fma.f64 (.f64 eps eps) (.f64 x x) (fma.f64 (pow.f64 x 3) 2/3 2)) (fma.f64 x x (.f64 (.f64 eps eps) (*.f64 (pow.f64 x 3) 2/3))))	eps	inf
5.0ms	(-.f64 (fma.f64 (.f64 eps eps) (.f64 x x) (fma.f64 (pow.f64 x 3) 2/3 2)) (fma.f64 x x (.f64 (.f64 eps eps) (*.f64 (pow.f64 x 3) 2/3))))	eps	0
4.0ms	(.f64 (.f64 eps eps) (*.f64 (pow.f64 x 3) 2/3))	x	-inf
3.0ms	(-.f64 (fma.f64 (.f64 eps eps) (.f64 x x) (fma.f64 (pow.f64 x 3) 2/3 2)) (fma.f64 x x (.f64 (.f64 eps eps) (*.f64 (pow.f64 x 3) 2/3))))	x	0

rewrite70.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

834×	`prod-diff_binary64`
156×	`add-sqr-sqrt_binary64`
150×	`pow1_binary64`
149×	`*-un-lft-identity_binary64`
146×	`add-log-exp_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	75
1	322	73
2	3868	73

Stop Event

1×	node limit

Counts

4 → 103

simplify56.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

738×	`cancel-sign-sub-inv_binary64`
398×	`fma-neg_binary64`
258×	`sub-neg_binary64`
243×	`*-commutative_binary64`
203×	`distribute-rgt-neg-in_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	31	1581
1	98	1479
2	351	1400
3	1639	1353
4	4777	1349

Stop Event

1×	node limit

Counts

187 → 130

prune132.0ms (3%)

Pruning

2 alts after pruning (0 fresh and 2 done)

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

Error

0.0b

Counts

132 → 2

Alt Table

Status	Error	Program
✓	20.5b	(/.f64 (-.f64 (fma.f64 (.f64 eps eps) (.f64 x x) (fma.f64 (pow.f64 x 3) 2/3 2)) (fma.f64 x x (.f64 (.f64 eps eps) (*.f64 (pow.f64 x 3) 2/3)))) 2)
✓	29.3b	(/.f64 (-.f64 (.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (.f64 (-.f64 1 eps) x)))) (.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (neg.f64 (.f64 (+.f64 1 eps) x))))) 2)

Status

Error

Program

✓

20.5b

(/.f64 (-.f64 (fma.f64 (*.f64 eps eps) (*.f64 x x) (fma.f64 (pow.f64 x 3) 2/3 2)) (fma.f64 x x (*.f64 (*.f64 eps eps) (*.f64 (pow.f64 x 3) 2/3)))) 2)

✓

29.3b

(/.f64 (-.f64 (*.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (*.f64 (-.f64 1 eps) x)))) (*.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (neg.f64 (*.f64 (+.f64 1 eps) x))))) 2)

Compiler

Compiled 4949 to 3277 computations (33.8% saved)

regimes183.0ms (4.1%)

Accuracy

Total 0.6b remaining (54.2%)

Threshold costs 0.6b (54.2%)

Counts

39 → 1

Compiler

Compiled 4220 to 3224 computations (23.6% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

7×	`+-commutative_binary64`
5×	`*-commutative_binary64`
5×	`sub-neg_binary64`
4×	`neg-sub0_binary64`
4×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	25
1	23	25
2	37	25
3	45	25
4	49	25
5	50	25

Stop Event

1×

saturated

end68.0ms (1.5%)

Stop Event

1×

done

Compiler

Compiled 97 to 66 computations (32% saved)

Details

analyze313.0ms (7%)

sample3.2s (70.6%)

preprocess38.0ms (0.9%)

simplify21.0ms (0.5%)

prune5.0ms (0.1%)

localize18.0ms (0.4%)

series50.0ms (1.1%)

rewrite62.0ms (1.4%)

simplify55.0ms (1.2%)

prune170.0ms (3.8%)

localize14.0ms (0.3%)

series59.0ms (1.3%)

rewrite70.0ms (1.6%)

simplify56.0ms (1.3%)

prune132.0ms (3%)

regimes183.0ms (4.1%)

simplify2.0ms (0.1%)

end68.0ms (1.5%)

Profiling