Details

analyze3.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	0%	100%	0
0%	0%	100%	1

Compiler

Compiled 53 to 38 computations (28.3% saved)

sample1.2s (14.8%)

Symmetry

(sort a b c d e)

Results

1.1s

8256×

body

128

valid

Compiler

Compiled 120 to 85 computations (29.2% saved)

simplify56.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

1006×	`rules-42_binary64`
1006×	`rules-43_binary64`
538×	`fma-neg_binary64`
466×	`fma-def_binary64`
254×	`rules-11_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	13
1	56	13
2	180	13
3	819	13
4	3856	13
5	5349	13

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

0.4b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.4b	(+.f64 (+.f64 (+.f64 (+.f64 e d) c) b) a)

Compiler

Compiled 42 to 27 computations (35.7% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.2b	(+.f64 (+.f64 e d) c)
✓	0.3b	(+.f64 (+.f64 (+.f64 e d) c) b)
✓	0.3b	(+.f64 (+.f64 (+.f64 (+.f64 e d) c) b) a)

series21.0ms (0.2%)

Counts

3 → 144

Calls

3 calls:

9.0ms	(+.f64 (+.f64 (+.f64 e d) c) b)
8.0ms	(+.f64 (+.f64 (+.f64 (+.f64 e d) c) b) a)
4.0ms	(+.f64 (+.f64 e d) c)

rewrite120.0ms (1.4%)

Algorithm

2×	batch-egg-rewrite

Rules

215×	`expm1-udef_binary64`
215×	`log1p-udef_binary64`
204×	`log-div_binary64`
186×	`log-pow_binary64`
150×	`egg-rr`

Counts

3 → 150

Calls

3 calls:

116.0ms	(+.f64 (+.f64 e d) c)
116.0ms	(+.f64 (+.f64 (+.f64 e d) c) b)
116.0ms	(+.f64 (+.f64 (+.f64 (+.f64 e d) c) b) a)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	30
1	255	30
2	3569	30
3	4977	30
4	5076	30
0	0	0
1	0	0

simplify98.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

821×	`rules-42_binary64`
821×	`rules-43_binary64`
663×	`rules-41_binary64`
417×	`fma-def_binary64`
376×	`rules-13_binary64`

Counts

294 → 168

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	1248
1	173	1248
2	712	1248
3	4035	1248
4	4903	1248
5	5299	1248

prune161.0ms (1.9%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	159	9	168
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	160	9	169

Error

Counts

169 → 9

Alt Table

Status	Error	Program
	1.2b	(pow.f64 (cbrt.f64 (+.f64 (+.f64 (+.f64 (+.f64 e d) c) b) a)) 3)
	0.5b	(+.f64 (.f64 (cbrt.f64 (.f64 b b)) (+.f64 (cbrt.f64 b) (/.f64 (+.f64 (+.f64 e d) c) (cbrt.f64 (*.f64 b b))))) a)
	0.6b	(/.f64 (+.f64 (+.f64 (pow.f64 (+.f64 (+.f64 e d) c) 3) (pow.f64 b 3)) (.f64 a (+.f64 (pow.f64 (+.f64 (+.f64 e d) c) 2) (-.f64 (.f64 b b) (.f64 (+.f64 (+.f64 e d) c) b))))) (+.f64 (pow.f64 (+.f64 (+.f64 e d) c) 2) (-.f64 (.f64 b b) (*.f64 (+.f64 (+.f64 e d) c) b))))
▶	0.4b	(+.f64 (*.f64 b (+.f64 1 (/.f64 (+.f64 (+.f64 e d) c) b))) a)
	0.5b	(.f64 (cbrt.f64 (.f64 a a)) (+.f64 (cbrt.f64 a) (/.f64 (+.f64 (+.f64 (+.f64 e d) c) b) (cbrt.f64 (*.f64 a a)))))
	0.5b	(+.f64 (+.f64 (*.f64 (+.f64 e d) (+.f64 1 (/.f64 c (+.f64 e d)))) b) a)
	0.5b	(*.f64 (+.f64 (+.f64 (+.f64 e d) c) b) (+.f64 1 (/.f64 a (+.f64 (+.f64 (+.f64 e d) c) b))))
	0.4b	(+.f64 c (+.f64 a (+.f64 d (+.f64 b e))))
	0.6b	(+.f64 (+.f64 (pow.f64 (sqrt.f64 (+.f64 (+.f64 e d) c)) 2) b) a)

Compiler

Compiled 3129 to 1046 computations (66.6% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(+.f64 (+.f64 e d) c)
✓	0.3b	(/.f64 (+.f64 (+.f64 e d) c) b)
✓	0.3b	(*.f64 b (+.f64 1 (/.f64 (+.f64 (+.f64 e d) c) b)))
✓	0.3b	(+.f64 (*.f64 b (+.f64 1 (/.f64 (+.f64 (+.f64 e d) c) b))) a)

series51.0ms (0.6%)

Counts

3 → 156

Calls

3 calls:

28.0ms	(*.f64 b (+.f64 1 (/.f64 (+.f64 (+.f64 e d) c) b)))
14.0ms	(/.f64 (+.f64 (+.f64 e d) c) b)
9.0ms	(+.f64 (*.f64 b (+.f64 1 (/.f64 (+.f64 (+.f64 e d) c) b))) a)

rewrite85.0ms (1%)

Algorithm

2×	batch-egg-rewrite

Rules

253×	`expm1-udef_binary64`
253×	`log1p-udef_binary64`
143×	`add-sqr-sqrt_binary64`
139×	`log1p-expm1-u_binary64`
139×	`expm1-log1p-u_binary64`

Counts

3 → 127

Calls

3 calls:

82.0ms	(/.f64 (+.f64 (+.f64 e d) c) b)
82.0ms	(*.f64 b (+.f64 1 (/.f64 (+.f64 (+.f64 e d) c) b)))
82.0ms	(+.f64 (*.f64 b (+.f64 1 (/.f64 (+.f64 (+.f64 e d) c) b))) a)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	33
1	322	33
2	4248	33
3	4973	33
0	0	0
1	0	0

simplify135.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

547×	`fma-def_binary64`
486×	`fma-neg_binary64`
440×	`rules-13_binary64`
255×	`rules-40_binary64`
255×	`rules-41_binary64`

Counts

283 → 158

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	40	1737
1	279	1728
2	1110	1476
3	4542	1476
4	4664	1476
5	4912	1476
6	5053	1476

prune209.0ms (2.5%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	210	1	211
Fresh	1	7	8
Picked	1	0	1
Done	0	0	0
Total	212	8	220

Error

Counts

220 → 8

Alt Table

Status	Error	Program
	0.5b	(.f64 (cbrt.f64 (.f64 a a)) (+.f64 (cbrt.f64 a) (/.f64 (+.f64 (+.f64 (+.f64 e d) c) b) (cbrt.f64 (*.f64 a a)))))
	0.5b	(+.f64 (+.f64 (*.f64 (+.f64 e d) (+.f64 1 (/.f64 c (+.f64 e d)))) b) a)
	0.5b	(*.f64 (+.f64 (+.f64 (+.f64 e d) c) b) (+.f64 1 (/.f64 a (+.f64 (+.f64 (+.f64 e d) c) b))))
	0.4b	(+.f64 c (+.f64 a (+.f64 d (+.f64 b e))))
	0.5b	(+.f64 (.f64 (cbrt.f64 (.f64 b b)) (+.f64 (cbrt.f64 b) (/.f64 (+.f64 (+.f64 e d) c) (cbrt.f64 (*.f64 b b))))) a)
	0.6b	(/.f64 (+.f64 (+.f64 (pow.f64 (+.f64 (+.f64 e d) c) 3) (pow.f64 b 3)) (.f64 a (+.f64 (pow.f64 (+.f64 (+.f64 e d) c) 2) (-.f64 (.f64 b b) (.f64 (+.f64 (+.f64 e d) c) b))))) (+.f64 (pow.f64 (+.f64 (+.f64 e d) c) 2) (-.f64 (.f64 b b) (*.f64 (+.f64 (+.f64 e d) c) b))))
▶	0.4b	(fma.f64 b (+.f64 1 (/.f64 (+.f64 (+.f64 e d) c) b)) a)
	0.6b	(+.f64 (+.f64 (pow.f64 (sqrt.f64 (+.f64 (+.f64 e d) c)) 2) b) a)

Compiler

Compiled 3896 to 1396 computations (64.2% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 1 (/.f64 (+.f64 (+.f64 e d) c) b))
✓	0.2b	(fma.f64 b (+.f64 1 (/.f64 (+.f64 (+.f64 e d) c) b)) a)
	0.2b	(+.f64 (+.f64 e d) c)
	0.3b	(/.f64 (+.f64 (+.f64 e d) c) b)

series57.0ms (0.7%)

Counts

2 → 108

Calls

2 calls:

36.0ms	(fma.f64 b (+.f64 1 (/.f64 (+.f64 (+.f64 e d) c) b)) a)
21.0ms	(+.f64 1 (/.f64 (+.f64 (+.f64 e d) c) b))

rewrite76.0ms (0.9%)

Algorithm

2×	batch-egg-rewrite

Rules

867×	`prod-diff_binary64`
129×	`add-sqr-sqrt_binary64`
124×	`log1p-expm1-u_binary64`
124×	`expm1-log1p-u_binary64`
119×	`add-log-exp_binary64`

Counts

2 → 73

Calls

2 calls:

72.0ms	(+.f64 1 (/.f64 (+.f64 (+.f64 e d) c) b))
72.0ms	(fma.f64 b (+.f64 1 (/.f64 (+.f64 (+.f64 e d) c) b)) a)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	30
1	289	26
2	3711	26
3	5436	26
0	0	0
1	0	0

simplify77.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

483×	`fma-def_binary64`
452×	`rules-13_binary64`
404×	`fma-neg_binary64`
250×	`rules-8-rev_binary64`
240×	`rules-40_binary64`

Counts

181 → 102

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	34	1404
1	245	1404
2	986	1179
3	4835	1179
4	4992	1179

prune168.0ms (2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	192	2	194
Fresh	2	5	7
Picked	0	1	1
Done	0	0	0
Total	194	8	202

Error

Counts

202 → 8

Alt Table

Status	Error	Program
▶	0.3b	(fma.f64 b (+.f64 1 (+.f64 (/.f64 d b) (+.f64 (/.f64 c b) (/.f64 e b)))) a)
	0.5b	(+.f64 (.f64 (cbrt.f64 (.f64 b b)) (+.f64 (cbrt.f64 b) (/.f64 (+.f64 (+.f64 e d) c) (cbrt.f64 (*.f64 b b))))) a)
	0.5b	(.f64 (cbrt.f64 (.f64 a a)) (+.f64 (cbrt.f64 a) (/.f64 (+.f64 (+.f64 (+.f64 e d) c) b) (cbrt.f64 (*.f64 a a)))))
	0.5b	(+.f64 (+.f64 (*.f64 (+.f64 e d) (+.f64 1 (/.f64 c (+.f64 e d)))) b) a)
	0.5b	(*.f64 (+.f64 (+.f64 (+.f64 e d) c) b) (+.f64 1 (/.f64 a (+.f64 (+.f64 (+.f64 e d) c) b))))
	0.6b	(/.f64 (+.f64 (+.f64 (pow.f64 (+.f64 (+.f64 e d) c) 3) (pow.f64 b 3)) (.f64 a (+.f64 (pow.f64 (+.f64 (+.f64 e d) c) 2) (-.f64 (.f64 b b) (.f64 (+.f64 (+.f64 e d) c) b))))) (+.f64 (pow.f64 (+.f64 (+.f64 e d) c) 2) (-.f64 (.f64 b b) (*.f64 (+.f64 (+.f64 e d) c) b))))
✓	0.4b	(fma.f64 b (+.f64 1 (/.f64 (+.f64 (+.f64 e d) c) b)) a)
	0.6b	(fma.f64 b (+.f64 1 (cbrt.f64 (pow.f64 (/.f64 (+.f64 (+.f64 e d) c) b) 3))) a)

Compiler

Compiled 3558 to 1295 computations (63.6% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 1 (+.f64 (/.f64 d b) (+.f64 (/.f64 c b) (/.f64 e b))))
✓	0.2b	(+.f64 (/.f64 d b) (+.f64 (/.f64 c b) (/.f64 e b)))
✓	0.2b	(+.f64 (/.f64 c b) (/.f64 e b))
✓	0.2b	(fma.f64 b (+.f64 1 (+.f64 (/.f64 d b) (+.f64 (/.f64 c b) (/.f64 e b)))) a)

series93.0ms (1.1%)

Counts

4 → 192

Calls

4 calls:

36.0ms	(fma.f64 b (+.f64 1 (+.f64 (/.f64 d b) (+.f64 (/.f64 c b) (/.f64 e b)))) a)
23.0ms	(+.f64 1 (+.f64 (/.f64 d b) (+.f64 (/.f64 c b) (/.f64 e b))))
21.0ms	(+.f64 (/.f64 d b) (+.f64 (/.f64 c b) (/.f64 e b)))
12.0ms	(+.f64 (/.f64 c b) (/.f64 e b))

rewrite96.0ms (1.2%)

Algorithm

2×	batch-egg-rewrite

Rules

275×	`log1p-udef_binary64`
188×	`egg-rr`
153×	`add-sqr-sqrt_binary64`
146×	`log1p-expm1-u_binary64`
146×	`expm1-log1p-u_binary64`

Counts

4 → 188

Calls

4 calls:

91.0ms	(+.f64 1 (+.f64 (/.f64 d b) (+.f64 (/.f64 c b) (/.f64 e b))))
91.0ms	(+.f64 (/.f64 d b) (+.f64 (/.f64 c b) (/.f64 e b)))
91.0ms	(+.f64 (/.f64 c b) (/.f64 e b))
91.0ms	(fma.f64 b (+.f64 1 (+.f64 (/.f64 d b) (+.f64 (/.f64 c b) (/.f64 e b)))) a)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	68
1	341	68
2	4605	68
3	5033	68
0	0	0
1	0	0

simplify144.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

522×	`fma-def_binary64`
494×	`rules-13_binary64`
454×	`fma-neg_binary64`
270×	`rules-40_binary64`
270×	`rules-41_binary64`

Counts

380 → 225

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	38	2412
1	269	2412
2	1078	2107
3	4707	1848
4	4168	1848
5	4715	1848
6	4872	1848

prune209.0ms (2.5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	224	1	225
Fresh	1	5	6
Picked	1	0	1
Done	0	1	1
Total	226	7	233

Error

Counts

233 → 7

Alt Table

Status	Error	Program
✓	0.4b	(fma.f64 b (+.f64 1 (/.f64 (+.f64 (+.f64 e d) c) b)) a)
	0.3b	(fma.f64 b (+.f64 1 (+.f64 (/.f64 d b) (fma.f64 (sqrt.f64 (/.f64 c b)) (sqrt.f64 (/.f64 c b)) (/.f64 e b)))) a)
	0.5b	(.f64 (cbrt.f64 (.f64 a a)) (+.f64 (cbrt.f64 a) (/.f64 (+.f64 (+.f64 (+.f64 e d) c) b) (cbrt.f64 (*.f64 a a)))))
	0.5b	(+.f64 (+.f64 (*.f64 (+.f64 e d) (+.f64 1 (/.f64 c (+.f64 e d)))) b) a)
	0.5b	(*.f64 (+.f64 (+.f64 (+.f64 e d) c) b) (+.f64 1 (/.f64 a (+.f64 (+.f64 (+.f64 e d) c) b))))
	0.5b	(+.f64 (.f64 (cbrt.f64 (.f64 b b)) (+.f64 (cbrt.f64 b) (/.f64 (+.f64 (+.f64 e d) c) (cbrt.f64 (*.f64 b b))))) a)
	0.6b	(fma.f64 b (+.f64 1 (cbrt.f64 (pow.f64 (/.f64 (+.f64 (+.f64 e d) c) b) 3))) a)

Compiler

Compiled 5445 to 1652 computations (69.7% saved)

regimes5.1s (60.9%)

Accuracy

Total 0.3b remaining (90.6%)

Threshold costs 0.3b (90.6%)

Counts

393 → 1

Compiler

Compiled 89101 to 56158 computations (37% saved)

simplify1.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	27
1	17	27
2	16	27

end112.0ms (1.4%)

Remove: (sort a b c d e)
Compiler: Compiled 253 to 155 computations (38.7% saved)

Details

analyze3.0ms (0%)

sample1.2s (14.8%)

simplify56.0ms (0.7%)

prune2.0ms (0%)

localize7.0ms (0.1%)

series21.0ms (0.2%)

rewrite120.0ms (1.4%)

simplify98.0ms (1.2%)

prune161.0ms (1.9%)

localize9.0ms (0.1%)

series51.0ms (0.6%)

rewrite85.0ms (1%)

simplify135.0ms (1.6%)

prune209.0ms (2.5%)

localize9.0ms (0.1%)

series57.0ms (0.7%)

rewrite76.0ms (0.9%)

simplify77.0ms (0.9%)

prune168.0ms (2%)

localize11.0ms (0.1%)

series93.0ms (1.1%)

rewrite96.0ms (1.2%)

simplify144.0ms (1.7%)

prune209.0ms (2.5%)

regimes5.1s (60.9%)

simplify1.0ms (0%)

end112.0ms (1.4%)

Profiling