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)

sample1.1s (17.7%)

Symmetry

(sort a b c d e)

Results

1.1s

8256×

body

128

valid

Compiler

Compiled 120 to 85 computations (29.2% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

128×	`associate-+l+_binary64`
99×	`associate-+r+_binary64`
56×	`+-commutative_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	13
1	20	13
2	56	13
3	143	13
4	188	13
5	186	13
6	186	13

prune1.0ms (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)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

series17.0ms (0.3%)

Counts

3 → 144

Calls

3 calls:

8.0ms	(+.f64 (+.f64 (+.f64 (+.f64 e d) c) b) a)
6.0ms	(+.f64 (+.f64 (+.f64 e d) c) b)
4.0ms	(+.f64 (+.f64 e d) c)

rewrite69.0ms (1.1%)

Algorithm

2×	batch-egg-rewrite

Rules

436×	`fma-neg_binary64`
236×	`expm1-udef_binary64`
236×	`log1p-udef_binary64`
156×	`hypot-def_binary64`
128×	`add-sqr-sqrt_binary64`

Counts

3 → 120

Calls

3 calls:

66.0ms	(+.f64 (+.f64 e d) c)
66.0ms	(+.f64 (+.f64 (+.f64 e d) c) b)
66.0ms	(+.f64 (+.f64 (+.f64 (+.f64 e d) c) b) a)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	30
1	242	30
2	3625	30
3	4987	30
0	0	0
1	0	0

simplify35.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

117×	`associate-+l+_binary64`
52×	`associate-+r+_binary64`
45×	`+-commutative_binary64`

Counts

264 → 138

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	1248
1	59	1248
2	132	1248
3	189	1248
4	186	1248
5	186	1248

prune122.0ms (1.9%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	131	7	138
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	132	7	139

Error

Counts

139 → 7

Alt Table

Status	Error	Program
	0.5b	(fma.f64 (sqrt.f64 (+.f64 (+.f64 e d) c)) (sqrt.f64 (+.f64 (+.f64 e d) c)) (+.f64 b a))
	0.5b	(+.f64 (+.f64 (/.f64 (+.f64 (pow.f64 (+.f64 e d) 3) (pow.f64 c 3)) (+.f64 (pow.f64 (+.f64 e d) 2) (*.f64 c (-.f64 c (+.f64 e d))))) b) a)
	0.4b	(+.f64 (/.f64 (-.f64 (pow.f64 (+.f64 e d) 2) (*.f64 (+.f64 c b) (+.f64 c b))) (-.f64 (+.f64 e d) (+.f64 c b))) a)
▶	0.4b	(+.f64 (+.f64 (fma.f64 1 e (+.f64 d c)) b) a)
	0.6b	(+.f64 (pow.f64 (sqrt.f64 (+.f64 (+.f64 (+.f64 e d) c) b)) 2) a)
	0.8b	(expm1.f64 (log1p.f64 (+.f64 (+.f64 (+.f64 (+.f64 e d) c) b) a)))
	1.0b	(+.f64 (+.f64 (fma.f64 (pow.f64 (cbrt.f64 (+.f64 e d)) 2) (cbrt.f64 (+.f64 e d)) c) b) a)

Compiler

Compiled 2560 to 846 computations (67% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

series21.0ms (0.3%)

Counts

3 → 144

Calls

3 calls:

9.0ms	(+.f64 (+.f64 (fma.f64 1 e (+.f64 d c)) b) a)
7.0ms	(+.f64 (fma.f64 1 e (+.f64 d c)) b)
5.0ms	(fma.f64 1 e (+.f64 d c))

rewrite65.0ms (1%)

Algorithm

2×	batch-egg-rewrite

Rules

623×	`fma-def_binary64`
304×	`fma-neg_binary64`
225×	`expm1-udef_binary64`
225×	`log1p-udef_binary64`
134×	`egg-rr`

Counts

3 → 134

Calls

3 calls:

62.0ms	(fma.f64 1 e (+.f64 d c))
62.0ms	(+.f64 (fma.f64 1 e (+.f64 d c)) b)
62.0ms	(+.f64 (+.f64 (fma.f64 1 e (+.f64 d c)) b) a)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	30
1	241	30
2	3236	30
3	5032	30
0	0	0
1	0	0

simplify34.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

117×	`associate-+l+_binary64`
52×	`associate-+r+_binary64`
45×	`+-commutative_binary64`

Counts

278 → 152

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	1248
1	59	1248
2	132	1248
3	189	1248
4	186	1248
5	186	1248

prune119.0ms (1.9%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	150	2	152
Fresh	3	3	6
Picked	1	0	1
Done	0	0	0
Total	154	5	159

Error

Counts

159 → 5

Alt Table

Status	Error	Program
	0.5b	(fma.f64 (sqrt.f64 (+.f64 (+.f64 e d) c)) (sqrt.f64 (+.f64 (+.f64 e d) c)) (+.f64 b a))
	0.5b	(+.f64 (+.f64 (/.f64 (+.f64 (pow.f64 (+.f64 e d) 3) (pow.f64 c 3)) (+.f64 (pow.f64 (+.f64 e d) 2) (*.f64 c (-.f64 c (+.f64 e d))))) b) a)
▶	0.2b	(fma.f64 1 e (+.f64 (+.f64 d c) (+.f64 b a)))
	0.4b	(fma.f64 (cbrt.f64 b) (cbrt.f64 (*.f64 b b)) (+.f64 (+.f64 e (+.f64 d c)) a))
	0.6b	(+.f64 (pow.f64 (sqrt.f64 (+.f64 (+.f64 (+.f64 e d) c) b)) 2) a)

Compiler

Compiled 2502 to 730 computations (70.8% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

series18.0ms (0.3%)

Counts

2 → 108

Calls

2 calls:

12.0ms	(fma.f64 1 e (+.f64 (+.f64 d c) (+.f64 b a)))
6.0ms	(+.f64 (+.f64 d c) (+.f64 b a))

rewrite62.0ms (1%)

Algorithm

2×	batch-egg-rewrite

Rules

703×	`fma-def_binary64`
343×	`fma-neg_binary64`
227×	`expm1-udef_binary64`
227×	`log1p-udef_binary64`
125×	`add-sqr-sqrt_binary64`

Counts

2 → 113

Calls

2 calls:

59.0ms	(fma.f64 1 e (+.f64 (+.f64 d c) (+.f64 b a)))
59.0ms	(+.f64 (+.f64 d c) (+.f64 b a))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	23
1	243	23
2	3378	23
3	5112	23
0	0	0
1	0	0

simplify31.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

131×	`associate-+l+_binary64`
56×	`associate-+r+_binary64`
41×	`+-commutative_binary64`

Counts

221 → 131

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	1041
1	57	1041
2	130	1041
3	187	1041
4	186	1041
5	186	1041

prune120.0ms (1.9%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	130	1	131
Fresh	1	3	4
Picked	0	1	1
Done	0	0	0
Total	131	5	136

Error

Counts

136 → 5

Alt Table

Status	Error	Program
	0.5b	(fma.f64 (sqrt.f64 (+.f64 (+.f64 e d) c)) (sqrt.f64 (+.f64 (+.f64 e d) c)) (+.f64 b a))
	0.5b	(+.f64 (+.f64 (/.f64 (+.f64 (pow.f64 (+.f64 e d) 3) (pow.f64 c 3)) (+.f64 (pow.f64 (+.f64 e d) 2) (*.f64 c (-.f64 c (+.f64 e d))))) b) a)
▶	0.4b	(fma.f64 1 e (fma.f64 (sqrt.f64 (+.f64 (+.f64 d c) b)) (sqrt.f64 (+.f64 (+.f64 d c) b)) a))
✓	0.2b	(fma.f64 1 e (+.f64 (+.f64 d c) (+.f64 b a)))
	0.4b	(fma.f64 (cbrt.f64 b) (cbrt.f64 (*.f64 b b)) (+.f64 (+.f64 e (+.f64 d c)) a))

Compiler

Compiled 2401 to 798 computations (66.8% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(sqrt.f64 (+.f64 (+.f64 d c) b))
✓	0.2b	(+.f64 (+.f64 d c) b)
✓	0.2b	(fma.f64 1 e (fma.f64 (sqrt.f64 (+.f64 (+.f64 d c) b)) (sqrt.f64 (+.f64 (+.f64 d c) b)) a))
✓	0.5b	(fma.f64 (sqrt.f64 (+.f64 (+.f64 d c) b)) (sqrt.f64 (+.f64 (+.f64 d c) b)) a)

series599.0ms (9.4%)

Counts

4 → 108

Calls

4 calls:

283.0ms	(fma.f64 1 e (fma.f64 (sqrt.f64 (+.f64 (+.f64 d c) b)) (sqrt.f64 (+.f64 (+.f64 d c) b)) a))
264.0ms	(fma.f64 (sqrt.f64 (+.f64 (+.f64 d c) b)) (sqrt.f64 (+.f64 (+.f64 d c) b)) a)
47.0ms	(sqrt.f64 (+.f64 (+.f64 d c) b))
4.0ms	(+.f64 (+.f64 d c) b)

rewrite67.0ms (1%)

Algorithm

2×	batch-egg-rewrite

Rules

514×	`fma-def_binary64`
258×	`fma-neg_binary64`
226×	`expm1-udef_binary64`
226×	`log1p-udef_binary64`
170×	`egg-rr`

Counts

4 → 170

Calls

4 calls:

63.0ms	(sqrt.f64 (+.f64 (+.f64 d c) b))
63.0ms	(+.f64 (+.f64 d c) b)
63.0ms	(fma.f64 1 e (fma.f64 (sqrt.f64 (+.f64 (+.f64 d c) b)) (sqrt.f64 (+.f64 (+.f64 d c) b)) a))
63.0ms	(fma.f64 (sqrt.f64 (+.f64 (+.f64 d c) b)) (sqrt.f64 (+.f64 (+.f64 d c) b)) a)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	39
1	250	39
2	3141	39
3	4947	39
0	0	0
1	0	0

simplify68.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

800×	`cancel-sign-sub-inv_binary64`
793×	`fma-neg_binary64`
472×	`*-commutative_binary64`
303×	`fma-def_binary64`
270×	`unswap-sqr_binary64`

Counts

278 → 214

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	98	1242
1	266	1232
2	703	1218
3	1914	1215
4	3351	1213
5	5138	1213

prune269.0ms (4.2%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	351	0	351
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	351	5	356

Error

Counts

356 → 5

Alt Table

Status	Error	Program
	0.5b	(fma.f64 (sqrt.f64 (+.f64 (+.f64 e d) c)) (sqrt.f64 (+.f64 (+.f64 e d) c)) (+.f64 b a))
	0.5b	(+.f64 (+.f64 (/.f64 (+.f64 (pow.f64 (+.f64 e d) 3) (pow.f64 c 3)) (+.f64 (pow.f64 (+.f64 e d) 2) (*.f64 c (-.f64 c (+.f64 e d))))) b) a)
✓	0.4b	(fma.f64 1 e (fma.f64 (sqrt.f64 (+.f64 (+.f64 d c) b)) (sqrt.f64 (+.f64 (+.f64 d c) b)) a))
✓	0.2b	(fma.f64 1 e (+.f64 (+.f64 d c) (+.f64 b a)))
	0.4b	(fma.f64 (cbrt.f64 b) (cbrt.f64 (*.f64 b b)) (+.f64 (+.f64 e (+.f64 d c)) a))

Compiler

Compiled 7865 to 2606 computations (66.9% saved)

regimes3.4s (53.3%)

Accuracy

Total 0.2b remaining (90.3%)

Threshold costs 0.2b (90.3%)

Counts

313 → 1

Compiler

Compiled 61055 to 37738 computations (38.2% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
1×	`*-commutative_binary64`
1×	`*-rgt-identity_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	19
1	18	19
2	17	19

end93.0ms (1.5%)

Remove: (sort a b c d e)
Compiler: Compiled 181 to 106 computations (41.4% saved)

Details

analyze3.0ms (0%)

sample1.1s (17.7%)

simplify7.0ms (0.1%)

prune1.0ms (0%)

localize6.0ms (0.1%)

series17.0ms (0.3%)

rewrite69.0ms (1.1%)

simplify35.0ms (0.5%)

prune122.0ms (1.9%)

localize7.0ms (0.1%)

series21.0ms (0.3%)

rewrite65.0ms (1%)

simplify34.0ms (0.5%)

prune119.0ms (1.9%)

localize7.0ms (0.1%)

series18.0ms (0.3%)

rewrite62.0ms (1%)

simplify31.0ms (0.5%)

prune120.0ms (1.9%)

localize8.0ms (0.1%)

series599.0ms (9.4%)

rewrite67.0ms (1%)

simplify68.0ms (1.1%)

prune269.0ms (4.2%)

regimes3.4s (53.3%)

simplify2.0ms (0%)

end93.0ms (1.5%)

Profiling