Details

analyze1.5s (26.1%)

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
0%	99.8%	0.2%	8
0%	99.8%	0.2%	9
0.4%	99.4%	0.2%	10
4.3%	95.5%	0.2%	11
6.4%	93.3%	0.2%	12
7.9%	91.9%	0.2%	13
13.7%	86%	0.2%	14

Compiler

Compiled 19 to 13 computations (31.6% saved)

sample1.3s (22.9%)

Results

1.2s	8254×	body	128	valid
70.0ms	527×	body	128	invalid
1.0ms	2×	body	512	valid

Compiler

Compiled 56 to 38 computations (32.1% saved)

simplify100.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

871×	`fma-neg_binary64`
683×	`sub-neg_binary64`
438×	`neg-mul-1_binary64`
412×	`neg-sub0_binary64`
378×	`distribute-rgt-out--_binary64`

Counts

1 → 2

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	13	19
1	28	19
2	66	19
3	158	17
4	344	17
5	846	17
6	2066	17
7	3773	17
8	4182	17
9	4701	17
10	4906	17
11	4923	17

prune4.0ms (0.1%)

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

2.7b

Counts

3 → 2

Alt Table

Status	Error	Program
	2.9b	(-.f64 x (/.f64 (-.f64 y z) (/.f64 (+.f64 (-.f64 t z) 1) a)))
▶	2.8b	(fma.f64 (/.f64 a (+.f64 (-.f64 t z) 1)) (-.f64 z y) x)

Compiler

Compiled 100 to 63 computations (37% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 a (+.f64 (-.f64 t z) 1))
✓	2.8b	(fma.f64 (/.f64 a (+.f64 (-.f64 t z) 1)) (-.f64 z y) x)

series97.0ms (1.7%)

Counts

2 → 96

Calls

2 calls:

56.0ms	(fma.f64 (/.f64 a (+.f64 (-.f64 t z) 1)) (-.f64 z y) x)
41.0ms	(/.f64 a (+.f64 (-.f64 t z) 1))

rewrite67.0ms (1.2%)

Algorithm

2×	batch-egg-rewrite

Rules

923×	`prod-diff_binary64`
140×	`add-sqr-sqrt_binary64`
134×	`log1p-expm1-u_binary64`
134×	`expm1-log1p-u_binary64`
130×	`add-log-exp_binary64`

Counts

2 → 58

Calls

2 calls:

65.0ms	(/.f64 a (+.f64 (-.f64 t z) 1))
65.0ms	(fma.f64 (/.f64 a (+.f64 (-.f64 t z) 1)) (-.f64 z y) x)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	27
1	269	27
2	3662	27
3	5548	27
0	0	0
1	0	0

simplify96.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

598×	`cancel-sign-sub-inv_binary64`
371×	`times-frac_binary64`
347×	`sub-neg_binary64`
318×	`associate-+r+_binary64`
271×	`+-commutative_binary64`

Counts

154 → 130

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	279	3917
1	882	3913
2	3755	3898
3	5215	3898

prune122.0ms (2.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	128	2	130
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	128	4	132

Error

0.0b

Counts

132 → 4

Alt Table

Status	Error	Program
▶	2.9b	(-.f64 x (/.f64 (-.f64 y z) (/.f64 (+.f64 (-.f64 t z) 1) a)))
	34.9b	(*.f64 a (-.f64 (/.f64 z (-.f64 (+.f64 1 t) z)) (/.f64 y (-.f64 (+.f64 1 t) z))))
	9.8b	(-.f64 (+.f64 (/.f64 (.f64 a z) (-.f64 (+.f64 1 t) z)) x) (/.f64 (.f64 y a) (-.f64 (+.f64 1 t) z)))
✓	2.8b	(fma.f64 (/.f64 a (+.f64 (-.f64 t z) 1)) (-.f64 z y) x)

Compiler

Compiled 4145 to 2022 computations (51.2% saved)

localize9.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (+.f64 (-.f64 t z) 1) a)
✓	10.0b	(/.f64 (-.f64 y z) (/.f64 (+.f64 (-.f64 t z) 1) a))

series72.0ms (1.3%)

Counts

2 → 84

Calls

2 calls:

61.0ms	(/.f64 (-.f64 y z) (/.f64 (+.f64 (-.f64 t z) 1) a))
11.0ms	(/.f64 (+.f64 (-.f64 t z) 1) a)

rewrite86.0ms (1.5%)

Algorithm

2×	batch-egg-rewrite

Rules

486×	`fma-def_binary64`
318×	`fma-neg_binary64`
241×	`log1p-udef_binary64`
239×	`expm1-udef_binary64`
135×	`add-sqr-sqrt_binary64`

Counts

2 → 97

Calls

2 calls:

83.0ms	(/.f64 (+.f64 (-.f64 t z) 1) a)
83.0ms	(/.f64 (-.f64 y z) (/.f64 (+.f64 (-.f64 t z) 1) a))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	26
1	259	26
2	3854	26
3	5369	26
0	0	0
1	0	0

simplify106.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

478×	`cancel-sign-sub-inv_binary64`
385×	`fma-neg_binary64`
371×	`times-frac_binary64`
278×	`sub-neg_binary64`
260×	`associate-+r+_binary64`

Counts

181 → 146

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	238	3235
1	759	3235
2	3268	2875
3	4582	2875
4	5004	2875

prune161.0ms (2.8%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	143	3	146
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	144	6	150

Error

Counts

150 → 6

Alt Table

Status	Error	Program
✓	2.8b	(fma.f64 (/.f64 a (+.f64 (-.f64 t z) 1)) (-.f64 z y) x)
▶	0.2b	(-.f64 x (*.f64 a (/.f64 (-.f64 y z) (+.f64 (-.f64 t z) 1))))
✓	2.9b	(-.f64 x (/.f64 (-.f64 y z) (/.f64 (+.f64 (-.f64 t z) 1) a)))
	9.8b	(-.f64 (+.f64 (/.f64 (.f64 a z) (-.f64 (+.f64 1 t) z)) x) (/.f64 (.f64 y a) (-.f64 (+.f64 1 t) z)))
	15.9b	(-.f64 x (fma.f64 (/.f64 (cbrt.f64 (*.f64 y y)) 1) (/.f64 (cbrt.f64 y) (/.f64 (+.f64 (-.f64 t z) 1) a)) (neg.f64 (/.f64 z (/.f64 (+.f64 (-.f64 t z) 1) a)))))
	3.1b	(-.f64 x (*.f64 (/.f64 (pow.f64 (cbrt.f64 (-.f64 y z)) 2) (+.f64 (-.f64 t z) 1)) (/.f64 (cbrt.f64 (-.f64 y z)) (/.f64 1 a))))

Compiler

Compiled 4703 to 2347 computations (50.1% saved)

localize10.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 y z) (+.f64 (-.f64 t z) 1))
✓	1.5b	(*.f64 a (/.f64 (-.f64 y z) (+.f64 (-.f64 t z) 1)))

series95.0ms (1.6%)

Counts

2 → 84

Calls

2 calls:

57.0ms	(*.f64 a (/.f64 (-.f64 y z) (+.f64 (-.f64 t z) 1)))
37.0ms	(/.f64 (-.f64 y z) (+.f64 (-.f64 t z) 1))

rewrite82.0ms (1.4%)

Algorithm

2×	batch-egg-rewrite

Rules

490×	`fma-def_binary64`
305×	`fma-neg_binary64`
235×	`log1p-udef_binary64`
233×	`expm1-udef_binary64`
131×	`add-sqr-sqrt_binary64`

Counts

2 → 75

Calls

2 calls:

81.0ms	(/.f64 (-.f64 y z) (+.f64 (-.f64 t z) 1))
81.0ms	(*.f64 a (/.f64 (-.f64 y z) (+.f64 (-.f64 t z) 1)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	29
1	253	29
2	3611	29
3	5097	29
0	0	0
1	0	0

simplify86.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

536×	`associate-+r+_binary64`
488×	`times-frac_binary64`
373×	`associate-+l+_binary64`
323×	`associate-/l*_binary64`
253×	`associate-/r*_binary64`

Counts

159 → 146

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	387	4680
1	1224	4670
2	5196	4670

prune168.0ms (2.9%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	144	2	146
Fresh	3	0	3
Picked	1	0	1
Done	0	2	2
Total	148	4	152

Error

Counts

152 → 4

Alt Table

Status	Error	Program
✓	2.9b	(-.f64 x (/.f64 (-.f64 y z) (/.f64 (+.f64 (-.f64 t z) 1) a)))
	0.3b	(-.f64 x (/.f64 a (/.f64 (+.f64 (-.f64 t z) 1) (-.f64 y z))))
▶	0.2b	(-.f64 x (*.f64 a (-.f64 (/.f64 y (+.f64 (-.f64 t z) 1)) (/.f64 z (+.f64 (-.f64 t z) 1)))))
✓	2.8b	(fma.f64 (/.f64 a (+.f64 (-.f64 t z) 1)) (-.f64 z y) x)

Compiler

Compiled 5742 to 2980 computations (48.1% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (/.f64 y (+.f64 (-.f64 t z) 1)) (/.f64 z (+.f64 (-.f64 t z) 1)))
✓	0.0b	(/.f64 y (+.f64 (-.f64 t z) 1))
✓	0.0b	(/.f64 z (+.f64 (-.f64 t z) 1))
✓	1.5b	(*.f64 a (-.f64 (/.f64 y (+.f64 (-.f64 t z) 1)) (/.f64 z (+.f64 (-.f64 t z) 1))))

series175.0ms (3.1%)

Counts

4 → 144

Calls

4 calls:

79.0ms	(*.f64 a (-.f64 (/.f64 y (+.f64 (-.f64 t z) 1)) (/.f64 z (+.f64 (-.f64 t z) 1))))
47.0ms	(-.f64 (/.f64 y (+.f64 (-.f64 t z) 1)) (/.f64 z (+.f64 (-.f64 t z) 1)))
32.0ms	(/.f64 y (+.f64 (-.f64 t z) 1))
17.0ms	(/.f64 z (+.f64 (-.f64 t z) 1))

rewrite114.0ms (2%)

Algorithm

2×	batch-egg-rewrite

Rules

410×	`fma-neg_binary64`
259×	`log1p-udef_binary64`
257×	`expm1-udef_binary64`
171×	`egg-rr`
144×	`add-sqr-sqrt_binary64`

Counts

4 → 171

Calls

4 calls:

108.0ms	(-.f64 (/.f64 y (+.f64 (-.f64 t z) 1)) (/.f64 z (+.f64 (-.f64 t z) 1)))
108.0ms	(/.f64 y (+.f64 (-.f64 t z) 1))
108.0ms	(/.f64 z (+.f64 (-.f64 t z) 1))
108.0ms	(*.f64 a (-.f64 (/.f64 y (+.f64 (-.f64 t z) 1)) (/.f64 z (+.f64 (-.f64 t z) 1))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	49
1	279	49
2	4128	49
3	5334	49
0	0	0
1	0	0

simplify117.0ms (2%)

Algorithm

1×	egg-herbie

Rules

528×	`associate-+l+_binary64`
507×	`times-frac_binary64`
340×	`associate-/l*_binary64`
276×	`associate--l+_binary64`
270×	`associate-/r*_binary64`

Counts

315 → 303

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	508	6963
1	1593	6951
2	5530	6951

prune308.0ms (5.4%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	303	0	303
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	303	4	307

Error

Counts

307 → 4

Alt Table

Status	Error	Program
✓	2.9b	(-.f64 x (/.f64 (-.f64 y z) (/.f64 (+.f64 (-.f64 t z) 1) a)))
	0.3b	(-.f64 x (/.f64 a (/.f64 (+.f64 (-.f64 t z) 1) (-.f64 y z))))
✓	0.2b	(-.f64 x (*.f64 a (-.f64 (/.f64 y (+.f64 (-.f64 t z) 1)) (/.f64 z (+.f64 (-.f64 t z) 1)))))
✓	2.8b	(fma.f64 (/.f64 a (+.f64 (-.f64 t z) 1)) (-.f64 z y) x)

Compiler

Compiled 11498 to 6066 computations (47.2% saved)

regimes761.0ms (13.2%)

Accuracy

Total 0.2b remaining (97.8%)

Threshold costs 0.2b (97.8%)

Counts

107 → 1

Compiler

Compiled 14520 to 9860 computations (32.1% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

11×	`+-commutative_binary64`
10×	`cancel-sign-sub-inv_binary64`
10×	`sub-neg_binary64`
9×	`neg-sub0_binary64`
9×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	28
1	27	28
2	43	28
3	57	28
4	79	28
5	94	28
6	99	28
7	100	28
8	96	28

end71.0ms (1.2%)

Compiler: Compiled 125 to 82 computations (34.4% saved)

Details

analyze1.5s (26.1%)

sample1.3s (22.9%)

simplify100.0ms (1.7%)

prune4.0ms (0.1%)

localize8.0ms (0.1%)

series97.0ms (1.7%)

rewrite67.0ms (1.2%)

simplify96.0ms (1.7%)

prune122.0ms (2.1%)

localize9.0ms (0.2%)

series72.0ms (1.3%)

rewrite86.0ms (1.5%)

simplify106.0ms (1.9%)

prune161.0ms (2.8%)

localize10.0ms (0.2%)

series95.0ms (1.6%)

rewrite82.0ms (1.4%)

simplify86.0ms (1.5%)

prune168.0ms (2.9%)

localize10.0ms (0.2%)

series175.0ms (3.1%)

rewrite114.0ms (2%)

simplify117.0ms (2%)

prune308.0ms (5.4%)

regimes761.0ms (13.2%)

simplify5.0ms (0.1%)

end71.0ms (1.2%)

Profiling