Details

analyze1.1s (9.7%)

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
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 (12.1%)

Results

1.2s	8033×	body	128	valid
72.0ms	564×	body	128	invalid
51.0ms	98×	body	1024	valid
32.0ms	77×	body	512	valid
10.0ms	47×	body	256	valid
1.0ms	1×	body	2048	valid

Compiler

Compiled 59 to 38 computations (35.6% saved)

simplify21.0ms (0.2%)

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

prune3.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

0.8b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.8b	(fma.f64 z (*.f64 y (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))) x)
	3.5b	(+.f64 x (.f64 (.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))))

Compiler

Compiled 107 to 60 computations (43.9% saved)

localize9.0ms (0.1%)

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 x y))
✓	1.8b	(*.f64 y (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))))

series614.0ms (5.4%)

Counts

4 → 144

Calls

4 calls:

236.0ms	(fma.f64 z (*.f64 y (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))) x)
177.0ms	(*.f64 y (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))))
149.0ms	(-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))
52.0ms	(tanh.f64 (/.f64 x y))

rewrite86.0ms (0.8%)

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

Calls

4 calls:

82.0ms	(fma.f64 z (*.f64 y (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))) x)
82.0ms	(-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))
82.0ms	(tanh.f64 (/.f64 x y))
82.0ms	(*.f64 y (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))))

simplify153.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

810×	`fma-def_binary64`
771×	`times-frac_binary64`
412×	`sub-neg_binary64`
191×	`fma-neg_binary64`
178×	`+-commutative_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	228	11622
1	774	10800
2	2681	10652

Stop Event

1×	node limit

Counts

318 → 271

prune193.0ms (1.7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	270	1	271
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	270	3	273

Error

0.0b

Counts

273 → 3

Alt Table

Status	Error	Program
✓	0.8b	(fma.f64 z (*.f64 y (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))) x)
▶	3.5b	(+.f64 x (.f64 (.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))))
	31.1b	(fma.f64 z (-.f64 t x) x)

Compiler

Compiled 10431 to 4033 computations (61.3% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (.f64 (.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))))
	0.0b	(-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))
	0.0b	(tanh.f64 (/.f64 x y))
✓	3.6b	(.f64 (.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))))

series513.0ms (4.5%)

Counts

2 → 96

Calls

2 calls:

299.0ms	(.f64 (.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))))
213.0ms	(+.f64 x (.f64 (.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))))

rewrite36.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

177×	`add-sqr-sqrt_binary64`
169×	`log1p-expm1-u_binary64`
169×	`expm1-log1p-u_binary64`
168×	`add-cbrt-cube_binary64`
165×	`add-log-exp_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	43
1	320	41

Stop Event

1×	node limit

Counts

2 → 56

Calls

2 calls:

35.0ms	(+.f64 x (.f64 (.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))))
35.0ms	(.f64 (.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y))))

simplify114.0ms (1%)

Algorithm

1×	egg-herbie

Rules

556×	`fma-def_binary64`
332×	`cancel-sign-sub-inv_binary64`
299×	`times-frac_binary64`
291×	`sub-neg_binary64`
257×	`associate-/l*_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	172	9431
1	579	8750
2	1897	7447

Stop Event

1×	node limit

Counts

152 → 118

prune234.0ms (2%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	284	1	285
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	284	4	288

Error

Counts

288 → 4

Alt Table

Status	Error	Program
✓	0.8b	(fma.f64 z (*.f64 y (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))) x)
✓	3.5b	(+.f64 x (.f64 (.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))))
	31.1b	(fma.f64 z (-.f64 t x) x)
▶	9.6b	(+.f64 x (/.f64 (.f64 (-.f64 (pow.f64 (tanh.f64 (/.f64 t y)) 3) (pow.f64 (tanh.f64 (/.f64 x y)) 3)) (.f64 y z)) (+.f64 (pow.f64 (tanh.f64 (/.f64 t y)) 2) (*.f64 (tanh.f64 (/.f64 x y)) (+.f64 (tanh.f64 (/.f64 x y)) (tanh.f64 (/.f64 t y)))))))

Compiler

Compiled 11242 to 4211 computations (62.5% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(pow.f64 (tanh.f64 (/.f64 t y)) 2)
✓	0.1b	(pow.f64 (tanh.f64 (/.f64 t y)) 3)
✓	3.6b	(.f64 (-.f64 (pow.f64 (tanh.f64 (/.f64 t y)) 3) (pow.f64 (tanh.f64 (/.f64 x y)) 3)) (.f64 y z))
✓	9.3b	(/.f64 (.f64 (-.f64 (pow.f64 (tanh.f64 (/.f64 t y)) 3) (pow.f64 (tanh.f64 (/.f64 x y)) 3)) (.f64 y z)) (+.f64 (pow.f64 (tanh.f64 (/.f64 t y)) 2) (*.f64 (tanh.f64 (/.f64 x y)) (+.f64 (tanh.f64 (/.f64 x y)) (tanh.f64 (/.f64 t y))))))

series5.5s (47.9%)

Counts

4 → 144

Calls

4 calls:

4.5s	(/.f64 (.f64 (-.f64 (pow.f64 (tanh.f64 (/.f64 t y)) 3) (pow.f64 (tanh.f64 (/.f64 x y)) 3)) (.f64 y z)) (+.f64 (pow.f64 (tanh.f64 (/.f64 t y)) 2) (*.f64 (tanh.f64 (/.f64 x y)) (+.f64 (tanh.f64 (/.f64 x y)) (tanh.f64 (/.f64 t y))))))
840.0ms	(.f64 (-.f64 (pow.f64 (tanh.f64 (/.f64 t y)) 3) (pow.f64 (tanh.f64 (/.f64 x y)) 3)) (.f64 y z))
81.0ms	(pow.f64 (tanh.f64 (/.f64 t y)) 3)
63.0ms	(pow.f64 (tanh.f64 (/.f64 t y)) 2)

rewrite42.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

251×	`log1p-expm1-u_binary64`
251×	`expm1-log1p-u_binary64`
247×	`add-cbrt-cube_binary64`
242×	`add-cube-cbrt_binary64`
242×	`add-log-exp_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	21	105
1	514	103

Stop Event

1×	node limit

Counts

4 → 58

Calls

4 calls:

41.0ms	(pow.f64 (tanh.f64 (/.f64 t y)) 2)
41.0ms	(pow.f64 (tanh.f64 (/.f64 t y)) 3)
40.0ms	(.f64 (-.f64 (pow.f64 (tanh.f64 (/.f64 t y)) 3) (pow.f64 (tanh.f64 (/.f64 x y)) 3)) (.f64 y z))
40.0ms	(/.f64 (.f64 (-.f64 (pow.f64 (tanh.f64 (/.f64 t y)) 3) (pow.f64 (tanh.f64 (/.f64 x y)) 3)) (.f64 y z)) (+.f64 (pow.f64 (tanh.f64 (/.f64 t y)) 2) (*.f64 (tanh.f64 (/.f64 x y)) (+.f64 (tanh.f64 (/.f64 x y)) (tanh.f64 (/.f64 t y))))))

simplify536.0ms (4.7%)

Algorithm

1×	egg-herbie

Rules

929×	`fma-def_binary64`
429×	`*-commutative_binary64`
310×	`+-commutative_binary64`
258×	`associate-+r+_binary64`
198×	`associate-/l*_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1155	59540
1	4634	58892

Stop Event

1×	node limit

Counts

202 → 148

prune556.0ms (4.9%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	148	0	148
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	148	4	152

Error

Counts

152 → 4

Alt Table

Status	Error	Program
✓	0.8b	(fma.f64 z (*.f64 y (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))) x)
✓	3.5b	(+.f64 x (.f64 (.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))))
▶	31.1b	(fma.f64 z (-.f64 t x) x)
✓	9.6b	(+.f64 x (/.f64 (.f64 (-.f64 (pow.f64 (tanh.f64 (/.f64 t y)) 3) (pow.f64 (tanh.f64 (/.f64 x y)) 3)) (.f64 y z)) (+.f64 (pow.f64 (tanh.f64 (/.f64 t y)) 2) (*.f64 (tanh.f64 (/.f64 x y)) (+.f64 (tanh.f64 (/.f64 x y)) (tanh.f64 (/.f64 t y)))))))

Compiler

Compiled 43191 to 18209 computations (57.8% saved)

localize4.0ms (0%)

Local error

Found 1 expressions with local error:

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

series7.0ms (0.1%)

Counts

1 → 36

Calls

1 calls:

7.0ms

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

rewrite74.0ms (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

Calls

1 calls:

73.0ms

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

simplify25.0ms (0.2%)

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

prune17.0ms (0.2%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	34	0	34
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	34	4	38

Error

Counts

38 → 4

Alt Table

Status	Error	Program
✓	0.8b	(fma.f64 z (*.f64 y (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))) x)
✓	3.5b	(+.f64 x (.f64 (.f64 y z) (-.f64 (tanh.f64 (/.f64 t y)) (tanh.f64 (/.f64 x y)))))
✓	31.1b	(fma.f64 z (-.f64 t x) x)
✓	9.6b	(+.f64 x (/.f64 (.f64 (-.f64 (pow.f64 (tanh.f64 (/.f64 t y)) 3) (pow.f64 (tanh.f64 (/.f64 x y)) 3)) (.f64 y z)) (+.f64 (pow.f64 (tanh.f64 (/.f64 t y)) 2) (*.f64 (tanh.f64 (/.f64 x y)) (+.f64 (tanh.f64 (/.f64 x y)) (tanh.f64 (/.f64 t y)))))))

Compiler

Compiled 416 to 144 computations (65.4% saved)

regimes113.0ms (1%)

Accuracy

Total 1.6b remaining (99%)

Threshold costs 0b (0%)

Counts

20 → 1

Compiler

Compiled 1563 to 981 computations (37.2% saved)

simplify6.0ms (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

end74.0ms (0.6%)

Compiler: Compiled 128 to 73 computations (43% saved)

Details

analyze1.1s (9.7%)

sample1.4s (12.1%)

simplify21.0ms (0.2%)

prune3.0ms (0%)

localize9.0ms (0.1%)

series614.0ms (5.4%)

rewrite86.0ms (0.8%)

simplify153.0ms (1.3%)

prune193.0ms (1.7%)

localize10.0ms (0.1%)

series513.0ms (4.5%)

rewrite36.0ms (0.3%)

simplify114.0ms (1%)

prune234.0ms (2%)

localize17.0ms (0.2%)

series5.5s (47.9%)

rewrite42.0ms (0.4%)

simplify536.0ms (4.7%)

prune556.0ms (4.9%)

localize4.0ms (0%)

series7.0ms (0.1%)

rewrite74.0ms (0.6%)

simplify25.0ms (0.2%)

prune17.0ms (0.2%)

regimes113.0ms (1%)

simplify6.0ms (0%)

end74.0ms (0.6%)

Profiling