Details

analyze1.7s (7.5%)

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)

sample1.3s (5.9%)

Results

1.1s	8019×	body	128	valid
78.0ms	575×	body	128	invalid
39.0ms	84×	body	1024	valid
35.0ms	110×	body	512	valid
10.0ms	43×	body	256	valid

Compiler

Compiled 59 to 38 computations (35.6% saved)

simplify40.0ms (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

2.9b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	2.9b	(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)

localize10.0ms (0%)

Local error

Found 4 expressions with local error:

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

series681.0ms (3.1%)

Counts

4 → 132

Calls

4 calls:

244.0ms	(-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))
237.0ms	(fma.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x)
125.0ms	(tanh.f64 (/.f64 x y))
75.0ms	(tanh.f64 (/.f64 t y))

rewrite15.0ms (0.1%)

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:

6.0ms	(-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))
3.0ms	(tanh.f64 (/.f64 x y))
1.0ms	(tanh.f64 (/.f64 t y))
0.0ms	(fma.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x)

simplify187.0ms (0.9%)

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 → 172

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	330	11824
1	1006	7805
2	3495	7805
3	5159	7805

prune126.0ms (0.6%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	169	3	172
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	170	3	173

Error

0.0b

Counts

173 → 3

Alt Table

Status	Error	Program
	22.2b	x
▶	10.5b	(fma.f64 (.f64 y z) (/.f64 (-.f64 (pow.f64 (tanh.f64 (/.f64 t y)) 3) (pow.f64 (tanh.f64 (/.f64 x y)) 3)) (fma.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 t y)) (.f64 (tanh.f64 (/.f64 x y)) (+.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))))) x)
	28.5b	(-.f64 (fma.f64 z t x) (*.f64 x z))

Compiler

Compiled 6666 to 2129 computations (68.1% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(pow.f64 (tanh.f64 (/.f64 t y)) 3)
✓	0.1b	(pow.f64 (tanh.f64 (/.f64 x y)) 3)
✓	2.7b	(fma.f64 (.f64 y z) (/.f64 (-.f64 (pow.f64 (tanh.f64 (/.f64 t y)) 3) (pow.f64 (tanh.f64 (/.f64 x y)) 3)) (fma.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 t y)) (.f64 (tanh.f64 (/.f64 x y)) (+.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))))) x)
✓	10.2b	(/.f64 (-.f64 (pow.f64 (tanh.f64 (/.f64 t y)) 3) (pow.f64 (tanh.f64 (/.f64 x y)) 3)) (fma.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 t y)) (*.f64 (tanh.f64 (/.f64 x y)) (+.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))))))

series14.3s (65.3%)

Counts

4 → 132

Calls

4 calls:

8.4s	(fma.f64 (.f64 y z) (/.f64 (-.f64 (pow.f64 (tanh.f64 (/.f64 t y)) 3) (pow.f64 (tanh.f64 (/.f64 x y)) 3)) (fma.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 t y)) (.f64 (tanh.f64 (/.f64 x y)) (+.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))))) x)
5.8s	(/.f64 (-.f64 (pow.f64 (tanh.f64 (/.f64 t y)) 3) (pow.f64 (tanh.f64 (/.f64 x y)) 3)) (fma.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 t y)) (*.f64 (tanh.f64 (/.f64 x y)) (+.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))))))
110.0ms	(pow.f64 (tanh.f64 (/.f64 t y)) 3)
100.0ms	(pow.f64 (tanh.f64 (/.f64 x y)) 3)

rewrite75.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

136×	`add-sqr-sqrt_binary64`
80×	`*-un-lft-identity_binary64`
75×	`times-frac_binary64`
64×	`difference-of-squares_binary64`
54×	`cube-prod_binary64`

Counts

4 → 195

Calls

4 calls:

22.0ms	(/.f64 (-.f64 (pow.f64 (tanh.f64 (/.f64 t y)) 3) (pow.f64 (tanh.f64 (/.f64 x y)) 3)) (fma.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 t y)) (*.f64 (tanh.f64 (/.f64 x y)) (+.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))))))
2.0ms	(pow.f64 (tanh.f64 (/.f64 t y)) 3)
2.0ms	(pow.f64 (tanh.f64 (/.f64 x y)) 3)
0.0ms	(fma.f64 (.f64 y z) (/.f64 (-.f64 (pow.f64 (tanh.f64 (/.f64 t y)) 3) (pow.f64 (tanh.f64 (/.f64 x y)) 3)) (fma.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 t y)) (.f64 (tanh.f64 (/.f64 x y)) (+.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))))) x)

simplify1.6s (7.3%)

Algorithm

1×	egg-herbie

Rules

468×	`fma-def_binary64`
398×	`associate-/r*_binary64`
299×	`associate-/l*_binary64`
295×	`times-frac_binary64`
94×	`sqr-pow_binary64`

Counts

327 → 280

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	2252	179661
1	5148	179661

prune1.5s (6.7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	280	0	280
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	280	3	283

Error

0.0b

Counts

283 → 3

Alt Table

Status	Error	Program
▶	22.2b	x
✓	10.5b	(fma.f64 (.f64 y z) (/.f64 (-.f64 (pow.f64 (tanh.f64 (/.f64 t y)) 3) (pow.f64 (tanh.f64 (/.f64 x y)) 3)) (fma.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 t y)) (.f64 (tanh.f64 (/.f64 x y)) (+.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))))) x)
	28.5b	(-.f64 (fma.f64 z t x) (*.f64 x z))

Compiler

Compiled 126873 to 48020 computations (62.2% saved)

localize1.0ms (0%)

prune4.0ms (0%)

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
✓	22.2b	x
✓	10.5b	(fma.f64 (.f64 y z) (/.f64 (-.f64 (pow.f64 (tanh.f64 (/.f64 t y)) 3) (pow.f64 (tanh.f64 (/.f64 x y)) 3)) (fma.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 t y)) (.f64 (tanh.f64 (/.f64 x y)) (+.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))))) x)
▶	28.5b	(-.f64 (fma.f64 z t x) (*.f64 x z))

Compiler

Compiled 75 to 37 computations (50.7% saved)

localize5.0ms (0%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	1.4b	(-.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:

3.0ms

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

simplify77.0ms (0.3%)

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

prune22.0ms (0.1%)

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
✓	22.2b	x
✓	10.5b	(fma.f64 (.f64 y z) (/.f64 (-.f64 (pow.f64 (tanh.f64 (/.f64 t y)) 3) (pow.f64 (tanh.f64 (/.f64 x y)) 3)) (fma.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 t y)) (.f64 (tanh.f64 (/.f64 x y)) (+.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))))) x)
✓	28.5b	(-.f64 (fma.f64 z t x) (*.f64 x z))

Compiler

Compiled 616 to 155 computations (74.8% saved)

regimes239.0ms (1.1%)

Accuracy

Total 2.4b remaining (98.7%)

Threshold costs 0b (0%)

Counts

42 → 2

Compiler

Compiled 4598 to 2631 computations (42.8% saved)

bsearch2.0ms (0%)

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

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	57
1	32	57
2	39	57
3	43	57
4	45	57
5	44	57

end70.0ms (0.3%)

Compiler: Compiled 147 to 66 computations (55.1% saved)

Details

analyze1.7s (7.5%)

sample1.3s (5.9%)

simplify40.0ms (0.2%)

prune3.0ms (0%)

localize10.0ms (0%)

series681.0ms (3.1%)

rewrite15.0ms (0.1%)

simplify187.0ms (0.9%)

prune126.0ms (0.6%)

localize18.0ms (0.1%)

series14.3s (65.3%)

rewrite75.0ms (0.3%)

simplify1.6s (7.3%)

prune1.5s (6.7%)

localize1.0ms (0%)

prune4.0ms (0%)

localize5.0ms (0%)

series8.0ms (0%)

rewrite3.0ms (0%)

simplify77.0ms (0.3%)

prune22.0ms (0.1%)

regimes239.0ms (1.1%)

bsearch2.0ms (0%)

simplify4.0ms (0%)

end70.0ms (0.3%)

Profiling