Details

analyze1.1s (20.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
6.2%	93.6%	0.2%	8
6.2%	93.6%	0.2%	9
10.1%	89.7%	0.2%	10
32%	67.8%	0.2%	11
39.4%	60.4%	0.2%	12
40.2%	59.6%	0.2%	13
47.5%	52.3%	0.2%	14

Compiler

Compiled 20 to 13 computations (35% saved)

sample1.4s (25.2%)

Results

1.3s	8015×	body	128	valid
77.0ms	567×	body	128	invalid
37.0ms	88×	body	1024	valid
30.0ms	91×	body	512	valid
15.0ms	60×	body	256	valid
1.0ms	2×	body	2048	valid

Compiler

Compiled 40 to 26 computations (35% saved)

preprocess70.0ms (1.2%)

Algorithm

2×	egg-herbie

Rules

525×	`distribute-rgt-in_binary64`
489×	`distribute-lft-in_binary64`
409×	`fma-def_binary64`
258×	`sub-neg_binary64`
130×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	50	161
1	243	147
2	722	147
3	2150	147
0	4	4

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 19 to 12 computations (36.8% saved)

simplify18.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

402×	`distribute-rgt-in_binary64`
372×	`distribute-lft-in_binary64`
289×	`fma-def_binary64`
256×	`associate-l_binary64`
255×	`associate-r_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	23
1	55	21
2	154	21
3	391	21
4	1460	21

Stop Event

1×	node limit

Counts

1 → 2

prune4.0ms (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

1.7b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	1.7b	(fma.f64 z (*.f64 y (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))) x)

Compiler

Compiled 69 to 36 computations (47.8% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 z (*.f64 y (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))) x)
✓	0.0b	(-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))
✓	0.0b	(tanh.f64 (/.f64 t y))
✓	2.7b	(*.f64 y (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))))

series619.0ms (10.9%)

Counts

4 → 144

Calls

36 calls:

35.0ms	(fma.f64 z (*.f64 y (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))) x)	t	inf
34.0ms	(fma.f64 z (*.f64 y (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))) x)	t	-inf
30.0ms	(*.f64 y (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))))	x	inf
28.0ms	(*.f64 y (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))))	x	-inf
28.0ms	(*.f64 y (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))))	t	-inf

rewrite105.0ms (1.8%)

Algorithm

1×	batch-egg-rewrite

Rules

569×	`prod-diff_binary64`
174×	`egg-rr`
161×	`add-sqr-sqrt_binary64`
152×	`log1p-expm1-u_binary64`
152×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	58
1	289	58
2	4496	58

Stop Event

1×	node limit

Counts

4 → 174

simplify181.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

823×	`fma-def_binary64`
771×	`times-frac_binary64`
410×	`sub-neg_binary64`
183×	`fma-neg_binary64`
179×	`+-commutative_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	228	11591
1	775	9996
2	2674	9844

Stop Event

1×	node limit

Counts

318 → 270

prune213.0ms (3.7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	268	2	270
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	268	3	271

Error

Counts

271 → 3

Alt Table

Status	Error	Program
✓	1.7b	(fma.f64 z (*.f64 y (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))) x)
▶	25.1b	(fma.f64 z (pow.f64 (sqrt.f64 (*.f64 y (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))))) 2) x)
	28.3b	(fma.f64 z (-.f64 t x) x)

Compiler

Compiled 10333 to 4033 computations (61% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (*.f64 y (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))))
	0.0b	(tanh.f64 (/.f64 t y))
✓	0.2b	(pow.f64 (sqrt.f64 (*.f64 y (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))))) 2)
	2.7b	(*.f64 y (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))))

series1.3s (22.7%)

Counts

2 → 64

Calls

18 calls:

625.0ms	(pow.f64 (sqrt.f64 (*.f64 y (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))))) 2)	y	0
196.0ms	(sqrt.f64 (*.f64 y (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))))	y	0
48.0ms	(pow.f64 (sqrt.f64 (*.f64 y (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))))) 2)	t	-inf
48.0ms	(pow.f64 (sqrt.f64 (*.f64 y (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))))) 2)	t	inf
47.0ms	(pow.f64 (sqrt.f64 (*.f64 y (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))))) 2)	x	inf

rewrite61.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

495×	`prod-diff_binary64`
157×	`add-sqr-sqrt_binary64`
151×	`log1p-expm1-u_binary64`
151×	`expm1-log1p-u_binary64`
149×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	36
1	313	36
2	4429	36

Stop Event

1×	node limit

Counts

2 → 63

simplify108.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

369×	`fma-def_binary64`
238×	`associate-+r+_binary64`
229×	`associate-/r*_binary64`
219×	`times-frac_binary64`
200×	`associate-r_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	376	8155
1	1263	7597

Stop Event

1×	node limit

Counts

127 → 131

prune183.0ms (3.2%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	222	0	222
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	222	3	225

Error

Counts

225 → 3

Alt Table

Status	Error	Program
✓	1.7b	(fma.f64 z (*.f64 y (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))) x)
✓	25.1b	(fma.f64 z (pow.f64 (sqrt.f64 (*.f64 y (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))))) 2) x)
▶	28.3b	(fma.f64 z (-.f64 t x) x)

Compiler

Compiled 11110 to 4641 computations (58.2% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 z (-.f64 t x) x)

series8.0ms (0.1%)

Counts

1 → 36

Calls

9 calls:

2.0ms	(fma.f64 z (-.f64 t x) x)	t	0
1.0ms	(fma.f64 z (-.f64 t x) x)	x	-inf
1.0ms	(fma.f64 z (-.f64 t x) x)	x	inf
1.0ms	(fma.f64 z (-.f64 t x) x)	z	-inf
1.0ms	(fma.f64 z (-.f64 t x) x)	t	-inf

rewrite36.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

686×	`log1p-expm1-u_binary64`
686×	`expm1-log1p-u_binary64`
423×	`prod-diff_binary64`
69×	`add-sqr-sqrt_binary64`
65×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	130	8
2	1775	8

Stop Event

1×	node limit

Counts

1 → 23

simplify26.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

267×	`fma-neg_binary64`
251×	`fma-def_binary64`
61×	`distribute-rgt-in_binary64`
37×	`associate--r+_binary64`
36×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	21	345
1	54	318
2	121	318
3	247	264
4	527	264
5	952	264
6	1139	264
7	1163	264

Stop Event

1×

saturated

Counts

59 → 34

prune16.0ms (0.3%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	34	0	34
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	34	3	37

Error

Counts

37 → 3

Alt Table

Status	Error	Program
✓	1.7b	(fma.f64 z (*.f64 y (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))) x)
✓	25.1b	(fma.f64 z (pow.f64 (sqrt.f64 (*.f64 y (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))))) 2) x)
✓	28.3b	(fma.f64 z (-.f64 t x) x)

Compiler

Compiled 373 to 124 computations (66.8% saved)

regimes95.0ms (1.7%)

Accuracy

Total 1.4b remaining (96.5%)

Threshold costs 0b (0%)

Counts

19 → 1

Compiler

Compiled 1568 to 946 computations (39.7% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	21
1	15	21
2	20	21
3	22	21
4	23	21

Stop Event

1×

saturated

end54.0ms (1%)

Stop Event

1×

done

Compiler

Compiled 85 to 53 computations (37.6% saved)

Details

analyze1.1s (20.1%)

sample1.4s (25.2%)

preprocess70.0ms (1.2%)

simplify18.0ms (0.3%)

prune4.0ms (0.1%)

localize10.0ms (0.2%)

series619.0ms (10.9%)

rewrite105.0ms (1.8%)

simplify181.0ms (3.2%)

prune213.0ms (3.7%)

localize12.0ms (0.2%)

series1.3s (22.7%)

rewrite61.0ms (1.1%)

simplify108.0ms (1.9%)

prune183.0ms (3.2%)

localize4.0ms (0.1%)

series8.0ms (0.1%)

rewrite36.0ms (0.6%)

simplify26.0ms (0.5%)

prune16.0ms (0.3%)

regimes95.0ms (1.7%)

simplify2.0ms (0%)

end54.0ms (1%)

Profiling