Details

analyze189.0ms (4.7%)

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
49.9%	49.9%	0.2%	3
49.9%	49.9%	0.2%	4
49.9%	49.9%	0.2%	5
49.9%	49.9%	0.2%	6
74.9%	25%	0.2%	7
74.9%	25%	0.2%	8
74.9%	25%	0.2%	9
74.9%	25%	0.2%	10
87.3%	12.5%	0.2%	11
87.3%	12.5%	0.2%	12
87.3%	12.5%	0.2%	13
87.3%	12.5%	0.2%	14

Compiler

Compiled 20 to 13 computations (35% saved)

sample1.5s (36.2%)

Infinites

5.8% of outputs are infinite.

Results

1.3s	8028×	body	128	valid
27.0ms	78×	body	512	valid
23.0ms	75×	body	1024	valid
12.0ms	73×	body	256	valid
1.0ms	2×	body	2048	valid

Compiler

Compiled 59 to 38 computations (35.6% saved)

simplify39.0ms (1%)

Algorithm

1×	egg-herbie

Rules

509×	`fma-neg_binary64`
396×	`distribute-rgt-in_binary64`
366×	`distribute-lft-in_binary64`
289×	`fma-def_binary64`
260×	`associate-l_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	23
1	55	21
2	153	21
3	362	21
4	1315	21
5	4639	21
6	5067	21

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

2.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	2.1b	(fma.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x)

Compiler

Compiled 69 to 35 computations (49.3% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(tanh.f64 (/.f64 x y))
✓	0.0b	(tanh.f64 (/.f64 t y))
✓	0.0b	(-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))
✓	2.1b	(fma.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x)

series558.0ms (13.9%)

Counts

4 → 132

Calls

4 calls:

269.0ms	(fma.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x)
160.0ms	(-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))
74.0ms	(tanh.f64 (/.f64 x y))
54.0ms	(tanh.f64 (/.f64 t y))

rewrite13.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`*-un-lft-identity_binary64`
14×	`add-sqr-sqrt_binary64`
12×	`add-cube-cbrt_binary64`
9×	`frac-sub_binary64`
9×	`prod-diff_binary64`

Counts

4 → 73

Calls

4 calls:

5.0ms	(-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))
1.0ms	(tanh.f64 (/.f64 t y))
1.0ms	(tanh.f64 (/.f64 x y))
0.0ms	(fma.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x)

simplify228.0ms (5.7%)

Algorithm

1×	egg-herbie

Rules

750×	`times-frac_binary64`
231×	`fma-neg_binary64`
202×	`fma-def_binary64`
174×	`distribute-rgt-in_binary64`
173×	`distribute-lft-in_binary64`

Counts

205 → 173

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	330	12435
1	1006	7805
2	3497	7805
3	5159	7805

prune112.0ms (2.8%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	170	3	173
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	171	3	174

Error

0.0b

Counts

174 → 3

Alt Table

Status	Error	Program
▶	2.1b	(fma.f64 (*.f64 y z) (log1p.f64 (expm1.f64 (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))))) x)
	28.4b	(-.f64 (fma.f64 z t x) (*.f64 x z))
	24.6b	x

Compiler

Compiled 6637 to 2121 computations (68% saved)

localize14.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))
✓	0.0b	(log1p.f64 (expm1.f64 (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))))
✓	0.2b	(expm1.f64 (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))))
✓	2.1b	(fma.f64 (*.f64 y z) (log1p.f64 (expm1.f64 (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))))) x)

series646.0ms (16.1%)

Counts

3 → 120

Calls

3 calls:

247.0ms

(expm1.f64 (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))))

232.0ms

(fma.f64 (*.f64 y z) (log1p.f64 (expm1.f64 (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))))) x)

166.0ms

(log1p.f64 (expm1.f64 (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))))

rewrite2.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`log1p-expm1-u_binary64`
3×	`*-un-lft-identity_binary64`
3×	`add-sqr-sqrt_binary64`
3×	`add-cube-cbrt_binary64`
3×	`add-cbrt-cube_binary64`

Counts

3 → 32

Calls

3 calls:

0.0ms

(fma.f64 (*.f64 y z) (log1p.f64 (expm1.f64 (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))))) x)

0.0ms

(expm1.f64 (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))))

0.0ms

(log1p.f64 (expm1.f64 (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))))

simplify224.0ms (5.6%)

Algorithm

1×	egg-herbie

Rules

439×	`cancel-sign-sub-inv_binary64`
409×	`sub-neg_binary64`
211×	`+-commutative_binary64`
206×	`fma-neg_binary64`
202×	`fma-def_binary64`

Counts

152 → 133

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	310	12668
1	945	9213
2	3426	8547
3	4957	8547

prune146.0ms (3.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	218	0	218
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	218	3	221

Error

0.0b

Counts

221 → 3

Alt Table

Status	Error	Program
✓	2.1b	(fma.f64 (*.f64 y z) (log1p.f64 (expm1.f64 (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))))) x)
	28.4b	(-.f64 (fma.f64 z t x) (*.f64 x z))
▶	24.6b	x

Compiler

Compiled 9698 to 3314 computations (65.8% saved)

localize1.0ms (0%)

prune2.0ms (0.1%)

Pruning

3 alts after pruning (1 fresh and 2 done)

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

Error

0.0b

Counts

3 → 3

Alt Table

Status	Error	Program
✓	2.1b	(fma.f64 (*.f64 y z) (log1p.f64 (expm1.f64 (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))))) x)
▶	28.4b	(-.f64 (fma.f64 z t x) (*.f64 x z))
✓	24.6b	x

Compiler

Compiled 49 to 31 computations (36.7% saved)

localize6.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	1.1b	(-.f64 (fma.f64 z t x) (*.f64 x z))

series7.0ms (0.2%)

Counts

1 → 36

Calls

1 calls:

7.0ms

(-.f64 (fma.f64 z t x) (*.f64 x z))

rewrite3.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`add-log-exp_binary64`
3×	`fma-neg_binary64`
3×	`*-un-lft-identity_binary64`
3×	`add-sqr-sqrt_binary64`
3×	`prod-diff_binary64`

Counts

1 → 21

Calls

1 calls:

2.0ms

(-.f64 (fma.f64 z t x) (*.f64 x z))

simplify76.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

625×	`fma-neg_binary64`
539×	`associate-+l+_binary64`
512×	`associate-+r+_binary64`
301×	`*-commutative_binary64`
241×	`neg-sub0_binary64`

Counts

57 → 42

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	60	695
1	142	615
2	415	596
3	1618	595
4	3553	508
5	4678	508
6	4933	508

prune24.0ms (0.6%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	42	0	42
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	42	3	45

Error

0.0b

Counts

45 → 3

Alt Table

Status	Error	Program
✓	2.1b	(fma.f64 (*.f64 y z) (log1p.f64 (expm1.f64 (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))))) x)
✓	28.4b	(-.f64 (fma.f64 z t x) (*.f64 x z))
✓	24.6b	x

Compiler

Compiled 590 to 149 computations (74.7% saved)

regimes182.0ms (4.5%)

Accuracy

Total 4.1b remaining (98.6%)

Threshold costs 0b (0%)

Counts

37 → 1

Compiler

Compiled 2618 to 1681 computations (35.8% saved)

simplify3.0ms (0.1%)

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	14	25
1	17	25
2	22	25
3	24	25
4	25	25
5	25	25

end75.0ms (1.9%)

Compiler: Compiled 77 to 50 computations (35.1% saved)

Details

analyze189.0ms (4.7%)

sample1.5s (36.2%)

simplify39.0ms (1%)

prune3.0ms (0.1%)

localize10.0ms (0.3%)

series558.0ms (13.9%)

rewrite13.0ms (0.3%)

simplify228.0ms (5.7%)

prune112.0ms (2.8%)

localize14.0ms (0.3%)

series646.0ms (16.1%)

rewrite2.0ms (0.1%)

simplify224.0ms (5.6%)

prune146.0ms (3.6%)

localize1.0ms (0%)

prune2.0ms (0.1%)

localize6.0ms (0.2%)

series7.0ms (0.2%)

rewrite3.0ms (0.1%)

simplify76.0ms (1.9%)

prune24.0ms (0.6%)

regimes182.0ms (4.5%)

simplify3.0ms (0.1%)

end75.0ms (1.9%)

Profiling