Details

analyze1.6s (17.9%)

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)

sample1.5s (16.6%)

Results

1.2s	8065×	body	128	valid
77.0ms	592×	body	128	invalid
66.0ms	79×	body	512	valid
32.0ms	67×	body	1024	valid
10.0ms	45×	body	256	valid

Compiler

Compiled 59 to 38 computations (35.6% saved)

simplify40.0ms (0.4%)

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

6.3b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	6.3b	(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 (0.1%)

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)))
✓	6.0b	(fma.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x)

series518.0ms (5.9%)

Counts

4 → 132

Calls

4 calls:

236.0ms	(fma.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x)
164.0ms	(-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))
59.0ms	(tanh.f64 (/.f64 t y))
58.0ms	(tanh.f64 (/.f64 x y))

rewrite12.0ms (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:

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)

simplify182.0ms (2.1%)

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

prune120.0ms (1.4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	170	3	173
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	170	4	174

Error

0.0b

Counts

174 → 4

Alt Table

Status	Error	Program
▶	6.3b	(fma.f64 (*.f64 y z) (log1p.f64 (expm1.f64 (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))))) x)
	26.9b	(-.f64 (fma.f64 z t x) (*.f64 x z))
✓	6.3b	(fma.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x)
	41.1b	(cbrt.f64 (.f64 (.f64 (fma.f64 (.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x) (fma.f64 (.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x)) (fma.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x)))

Compiler

Compiled 6743 to 2152 computations (68.1% saved)

localize12.0ms (0.1%)

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))))
✓	6.0b	(fma.f64 (*.f64 y z) (log1p.f64 (expm1.f64 (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))))) x)

series601.0ms (6.8%)

Counts

3 → 120

Calls

3 calls:

256.0ms

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

190.0ms

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

154.0ms

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

rewrite2.0ms (0%)

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)))))

simplify189.0ms (2.1%)

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

prune159.0ms (1.8%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	218	0	218
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	218	4	222

Error

0.0b

Counts

222 → 4

Alt Table

Status	Error	Program
✓	6.3b	(fma.f64 (*.f64 y z) (log1p.f64 (expm1.f64 (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))))) x)
▶	26.9b	(-.f64 (fma.f64 z t x) (*.f64 x z))
✓	6.3b	(fma.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x)
	41.1b	(cbrt.f64 (.f64 (.f64 (fma.f64 (.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x) (fma.f64 (.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x)) (fma.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x)))

Compiler

Compiled 9804 to 3345 computations (65.9% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

series7.0ms (0.1%)

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))

simplify79.0ms (0.9%)

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

prune21.0ms (0.2%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	42	0	42
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	42	4	46

Error

0.0b

Counts

46 → 4

Alt Table

Status	Error	Program
✓	6.3b	(fma.f64 (*.f64 y z) (log1p.f64 (expm1.f64 (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))))) x)
✓	26.9b	(-.f64 (fma.f64 z t x) (*.f64 x z))
✓	6.3b	(fma.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x)
▶	41.1b	(cbrt.f64 (.f64 (.f64 (fma.f64 (.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x) (fma.f64 (.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x)) (fma.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x)))

Compiler

Compiled 701 to 184 computations (73.8% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (.f64 (fma.f64 (.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x) (fma.f64 (.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x)) (fma.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x))
✓	0.2b	(.f64 (fma.f64 (.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x) (fma.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x))
	6.0b	(fma.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x)
✓	37.9b	(cbrt.f64 (.f64 (.f64 (fma.f64 (.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x) (fma.f64 (.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x)) (fma.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x)))

series1.9s (21.6%)

Counts

3 → 144

Calls

3 calls:

1.3s

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

422.0ms

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

232.0ms

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

rewrite20.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`pow1_binary64`
13×	`add-cbrt-cube_binary64`
11×	`add-sqr-sqrt_binary64`
10×	`add-exp-log_binary64`
8×	`*-un-lft-identity_binary64`

Counts

3 → 74

Calls

3 calls:

4.0ms

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

3.0ms

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

3.0ms

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

simplify870.0ms (9.8%)

Algorithm

1×	egg-herbie

Rules

708×	`associate-+r+_binary64`
614×	`fma-def_binary64`
217×	`associate-r_binary64`
198×	`associate-/l*_binary64`
191×	`associate-*r/_binary64`

Counts

218 → 236

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1695	62689
1	5325	62689

prune656.0ms (7.4%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	365	0	365
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	365	4	369

Error

0.0b

Counts

369 → 4

Alt Table

Status	Error	Program
✓	6.3b	(fma.f64 (*.f64 y z) (log1p.f64 (expm1.f64 (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))))) x)
✓	26.9b	(-.f64 (fma.f64 z t x) (*.f64 x z))
✓	6.3b	(fma.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x)
✓	41.1b	(cbrt.f64 (.f64 (.f64 (fma.f64 (.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x) (fma.f64 (.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x)) (fma.f64 (*.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))) x)))

Compiler

Compiled 75386 to 24171 computations (67.9% saved)

regimes284.0ms (3.2%)

Accuracy

Total 0.7b remaining (75.1%)

Threshold costs 0.7b (75.1%)

Counts

40 → 3

Compiler

Compiled 4288 to 2361 computations (44.9% saved)

bsearch2.0ms (0%)

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

simplify5.0ms (0.1%)

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	24	99
1	35	99
2	48	99
3	56	99
4	61	99
5	62	99
6	62	99

end78.0ms (0.9%)

Compiler: Compiled 239 to 89 computations (62.8% saved)

Details

analyze1.6s (17.9%)

sample1.5s (16.6%)

simplify40.0ms (0.4%)

prune3.0ms (0%)

localize11.0ms (0.1%)

series518.0ms (5.9%)

rewrite12.0ms (0.1%)

simplify182.0ms (2.1%)

prune120.0ms (1.4%)

localize12.0ms (0.1%)

series601.0ms (6.8%)

rewrite2.0ms (0%)

simplify189.0ms (2.1%)

prune159.0ms (1.8%)

localize5.0ms (0.1%)

series7.0ms (0.1%)

rewrite3.0ms (0%)

simplify79.0ms (0.9%)

prune21.0ms (0.2%)

localize12.0ms (0.1%)

series1.9s (21.6%)

rewrite20.0ms (0.2%)

simplify870.0ms (9.8%)

prune656.0ms (7.4%)

regimes284.0ms (3.2%)

bsearch2.0ms (0%)

simplify5.0ms (0.1%)

end78.0ms (0.9%)

Profiling