Details

analyze1.6s (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
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
7.8%	92%	0.2%	8
7.8%	92%	0.2%	9
10.9%	88.9%	0.2%	10
34.7%	65.1%	0.2%	11
43.1%	56.7%	0.2%	12
44.2%	55.7%	0.2%	13
49.5%	50.3%	0.2%	14

Compiler

Compiled 20 to 13 computations (35% saved)

sample68.0ms (0.3%)

Algorithm

1×

intervals

Results

17.0ms	253×	body	128	valid
1.0ms	19×	body	128	invalid
0.0ms	2×	body	256	valid
0.0ms	1×	body	512	valid

Compiler

Compiled 43 to 29 computations (32.6% saved)

simplify37.0ms (0.2%)

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%)

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

3.9b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	3.9b	(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)

localize11.0ms (0%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(tanh.f64 (/.f64 t y))
✓	0.2b	(-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))
✓	3.7b	(fma.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x)

series531.0ms (2.4%)

Counts

3 → 108

Calls

3 calls:

298.0ms	(fma.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x)
173.0ms	(-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))
59.0ms	(tanh.f64 (/.f64 t y))

rewrite13.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 61

Calls

3 calls:

7.0ms	(-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))
2.0ms	(fma.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x)
1.0ms	(tanh.f64 (/.f64 t y))

simplify176.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

747×	`times-frac_binary64`
202×	`fma-neg_binary64`
200×	`fma-def_binary64`
174×	`distribute-rgt-in_binary64`
173×	`distribute-lft-in_binary64`

Counts

169 → 146

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	320	10873
1	986	8101
2	3401	8101
3	4985	8101

prune99.0ms (0.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	144	2	146
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	144	3	147

Error

Counts

147 → 3

Alt Table

Status	Error	Program
	27.9b	(-.f64 (fma.f64 z t x) (*.f64 x z))
✓	3.9b	(fma.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x)
▶	5.1b	(.f64 (.f64 (cbrt.f64 (fma.f64 (.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x)) (cbrt.f64 (fma.f64 (.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x))) (cbrt.f64 (fma.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x)))

Compiler

Compiled 6025 to 1955 computations (67.6% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (.f64 (cbrt.f64 (fma.f64 (.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x)) (cbrt.f64 (fma.f64 (.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x))) (cbrt.f64 (fma.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x)))
✓	0.5b	(.f64 (cbrt.f64 (fma.f64 (.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x)) (cbrt.f64 (fma.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x)))
✓	0.6b	(cbrt.f64 (fma.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x))
	3.7b	(fma.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x)

series14.8s (66.7%)

Counts

3 → 144

Calls

3 calls:

10.5s

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

4.0s

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

262.0ms

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

rewrite23.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`pow1_binary64`
24×	`add-sqr-sqrt_binary64`
23×	`cbrt-prod_binary64`
16×	`pow1/3_binary64`
14×	`*-un-lft-identity_binary64`

Counts

3 → 93

Calls

3 calls:

8.0ms

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

4.0ms

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

1.0ms

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

simplify1.2s (5.4%)

Algorithm

1×	egg-herbie

Rules

851×	`fma-def_binary64`
259×	`times-frac_binary64`
70×	`sub-neg_binary64`
36×	`unpow1/3_binary64`
15×	`unpow2_binary64`

Counts

237 → 257

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3399	130947
1	5047	130947

prune2.3s (10.3%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	548	0	548
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	548	3	551

Error

Counts

551 → 3

Alt Table

Status	Error	Program
▶	27.9b	(-.f64 (fma.f64 z t x) (*.f64 x z))
✓	3.9b	(fma.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x)
✓	5.1b	(.f64 (.f64 (cbrt.f64 (fma.f64 (.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x)) (cbrt.f64 (fma.f64 (.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x))) (cbrt.f64 (fma.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x)))

Compiler

Compiled 233634 to 75814 computations (67.6% saved)

localize5.0ms (0%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.5b	(-.f64 (fma.f64 z t x) (*.f64 x z))

series8.0ms (0%)

Counts

1 → 36

Calls

1 calls:

7.0ms

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

rewrite3.0ms (0%)

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))

simplify80.0ms (0.4%)

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

prune39.0ms (0.2%)

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

Counts

45 → 3

Alt Table

Status	Error	Program
✓	27.9b	(-.f64 (fma.f64 z t x) (*.f64 x z))
✓	3.9b	(fma.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x)
✓	5.1b	(.f64 (.f64 (cbrt.f64 (fma.f64 (.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x)) (cbrt.f64 (fma.f64 (.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x))) (cbrt.f64 (fma.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x)))

Compiler

Compiled 634 to 157 computations (75.2% saved)

regimes198.0ms (0.9%)

Accuracy

Total 2.1b remaining (93.4%)

Threshold costs 0b (0%)

Counts

28 → 2

Compiler

Compiled 2593 to 1481 computations (42.9% saved)

bsearch1.0ms (0%)

Compiler: Compiled 19 to 12 computations (36.8% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	60
1	32	60
2	45	60
3	53	60
4	58	60
5	59	60
6	59	60

end1.0ms (0%)

Compiler: Compiled 44 to 19 computations (56.8% saved)

sample1.0s (4.7%)

Algorithm

1×

intervals

Results

571.0ms	7803×	body	128	valid
39.0ms	511×	body	128	invalid
26.0ms	70×	body	1024	valid
17.0ms	82×	body	512	valid
9.0ms	45×	body	256	valid

Compiler

Compiled 149 to 68 computations (54.4% saved)

Details

analyze1.6s (7%)

sample68.0ms (0.3%)

simplify37.0ms (0.2%)

prune3.0ms (0%)

localize11.0ms (0%)

series531.0ms (2.4%)

rewrite13.0ms (0.1%)

simplify176.0ms (0.8%)

prune99.0ms (0.4%)

localize13.0ms (0.1%)

series14.8s (66.7%)

rewrite23.0ms (0.1%)

simplify1.2s (5.4%)

prune2.3s (10.3%)

localize5.0ms (0%)

series8.0ms (0%)

rewrite3.0ms (0%)

simplify80.0ms (0.4%)

prune39.0ms (0.2%)

regimes198.0ms (0.9%)

bsearch1.0ms (0%)

simplify4.0ms (0%)

end1.0ms (0%)

sample1.0s (4.7%)

Profiling