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 (18.7%)

Symmetry

(sort a b c d e)

Results

1.2s

8256×

body

128

valid

Compiler

Compiled 120 to 85 computations (29.2% saved)

simplify8.0ms (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

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)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.2b	(+.f64 (+.f64 (+.f64 e d) c) b)
✓	0.2b	(+.f64 (+.f64 e d) c)
✓	0.2b	(+.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)
5.0ms	(+.f64 (+.f64 (+.f64 e d) c) b)
4.0ms	(+.f64 (+.f64 e d) c)

rewrite88.0ms (1.4%)

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 → 123

Calls

3 calls:

86.0ms	(+.f64 (+.f64 (+.f64 e d) c) b)
86.0ms	(+.f64 (+.f64 e d) c)
86.0ms	(+.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

simplify39.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

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

Counts

267 → 141

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

prune132.0ms (2%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	134	7	141
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	135	7	142

Error

Counts

142 → 7

Alt Table

Status	Error	Program
▶	0.3b	(fma.f64 1 (+.f64 (+.f64 e d) c) (+.f64 b a))
	0.6b	(/.f64 1 (/.f64 (+.f64 (pow.f64 (+.f64 (+.f64 (+.f64 e d) c) b) 2) (*.f64 a (-.f64 a (+.f64 (+.f64 (+.f64 e d) c) b)))) (+.f64 (pow.f64 (+.f64 (+.f64 (+.f64 e d) c) b) 3) (pow.f64 a 3))))
	1.1b	(pow.f64 (pow.f64 (+.f64 (+.f64 (+.f64 (+.f64 e d) c) b) a) 3) 1/3)
	0.4b	(+.f64 c (+.f64 a (+.f64 d (+.f64 b e))))
	0.6b	(+.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)
	0.5b	(+.f64 (+.f64 (fma.f64 (cbrt.f64 (*.f64 e e)) (cbrt.f64 e) (+.f64 d c)) b) a)
	0.6b	(+.f64 (-.f64 (/.f64 (pow.f64 (+.f64 (+.f64 e d) c) 2) (-.f64 (+.f64 (+.f64 e d) c) b)) (/.f64 (*.f64 b b) (-.f64 (+.f64 (+.f64 e d) c) b))) a)

Compiler

Compiled 2637 to 869 computations (67% saved)

localize11.0ms (0.2%)

Local error

Found 2 expressions with local error:

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

series10.0ms (0.2%)

Counts

1 → 60

Calls

1 calls:

10.0ms

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

rewrite54.0ms (0.8%)

Algorithm

2×	batch-egg-rewrite

Rules

631×	`fma-def_binary64`
299×	`fma-neg_binary64`
225×	`expm1-udef_binary64`
225×	`log1p-udef_binary64`
124×	`add-sqr-sqrt_binary64`

Counts

1 → 31

Calls

1 calls:

53.0ms

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	13
1	241	13
2	3254	13
3	4969	13
0	0	0
1	0	0

simplify23.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

125×	`associate-+l+_binary64`
60×	`associate-+r+_binary64`
52×	`+-commutative_binary64`

Counts

91 → 42

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	645
1	46	645
2	121	645
3	187	645
4	186	645
5	186	645

prune75.0ms (1.2%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	85	2	87
Fresh	3	3	6
Picked	0	1	1
Done	0	0	0
Total	88	6	94

Error

Counts

94 → 6

Alt Table

Status	Error	Program
✓	0.3b	(fma.f64 1 (+.f64 (+.f64 e d) c) (+.f64 b a))
▶	0.3b	(+.f64 e (+.f64 (+.f64 d c) (+.f64 b a)))
	0.5b	(fma.f64 1 (/.f64 (+.f64 (pow.f64 e 3) (pow.f64 (+.f64 d c) 3)) (+.f64 (.f64 e e) (-.f64 (.f64 (+.f64 d c) (+.f64 d c)) (*.f64 e (+.f64 d c))))) (+.f64 b a))
	1.1b	(pow.f64 (pow.f64 (+.f64 (+.f64 (+.f64 (+.f64 e d) c) b) a) 3) 1/3)
	0.4b	(+.f64 c (+.f64 a (+.f64 d (+.f64 b e))))
	0.6b	(+.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)

Compiler

Compiled 1607 to 574 computations (64.3% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

series13.0ms (0.2%)

Counts

2 → 108

Calls

2 calls:

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

rewrite79.0ms (1.2%)

Algorithm

2×	batch-egg-rewrite

Rules

906×	`fma-def_binary64`
436×	`fma-neg_binary64`
236×	`expm1-udef_binary64`
236×	`log1p-udef_binary64`
158×	`egg-rr`

Counts

2 → 158

Calls

2 calls:

76.0ms	(+.f64 e (+.f64 (+.f64 d c) (+.f64 b a)))
76.0ms	(+.f64 (+.f64 d c) (+.f64 b a))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	23
1	242	23
2	3705	23
3	5786	23
0	0	0
1	0	0

simplify97.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

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

Counts

266 → 176

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

prune178.0ms (2.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	173	3	176
Fresh	3	1	4
Picked	0	1	1
Done	1	0	1
Total	177	5	182

Error

Counts

182 → 5

Alt Table

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

Compiler

Compiled 3201 to 894 computations (72.1% saved)

localize19.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(+.f64 (+.f64 b a) e)
✓	0.2b	(+.f64 (pow.f64 d 3) (pow.f64 c 3))
✓	0.2b	(fma.f64 (+.f64 (pow.f64 d 3) (pow.f64 c 3)) (/.f64 1 (fma.f64 d d (*.f64 c (-.f64 c d)))) (+.f64 (+.f64 b a) e))
✓	0.3b	(/.f64 1 (fma.f64 d d (*.f64 c (-.f64 c d))))

series204.0ms (3.1%)

Counts

4 → 144

Calls

4 calls:

176.0ms	(fma.f64 (+.f64 (pow.f64 d 3) (pow.f64 c 3)) (/.f64 1 (fma.f64 d d (*.f64 c (-.f64 c d)))) (+.f64 (+.f64 b a) e))
10.0ms	(/.f64 1 (fma.f64 d d (*.f64 c (-.f64 c d))))
9.0ms	(+.f64 (pow.f64 d 3) (pow.f64 c 3))
7.0ms	(+.f64 (+.f64 b a) e)

rewrite95.0ms (1.5%)

Algorithm

2×	batch-egg-rewrite

Rules

597×	`prod-diff_binary64`
205×	`add-sqr-sqrt_binary64`
197×	`log1p-expm1-u_binary64`
197×	`expm1-log1p-u_binary64`
191×	`add-cbrt-cube_binary64`

Counts

4 → 118

Calls

4 calls:

92.0ms	(+.f64 (+.f64 b a) e)
92.0ms	(+.f64 (pow.f64 d 3) (pow.f64 c 3))
92.0ms	(fma.f64 (+.f64 (pow.f64 d 3) (pow.f64 c 3)) (/.f64 1 (fma.f64 d d (*.f64 c (-.f64 c d)))) (+.f64 (+.f64 b a) e))
92.0ms	(/.f64 1 (fma.f64 d d (*.f64 c (-.f64 c d))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	64
1	407	63
2	4690	63
3	5896	63
0	0	0
1	0	0

simplify99.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

772×	`associate-/r*_binary64`
504×	`cancel-sign-sub-inv_binary64`
447×	`fma-def_binary64`
442×	`fma-neg_binary64`
306×	`div-sub_binary64`

Counts

262 → 160

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	64	2862
1	163	2562
2	476	2562
3	1522	2562
4	4392	2562
5	5059	2562

prune154.0ms (2.4%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	159	1	160
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	160	5	165

Error

Counts

165 → 5

Alt Table

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

Compiler

Compiled 4583 to 1959 computations (57.3% saved)

regimes3.8s (57.8%)

Accuracy

Total 0.2b remaining (97.5%)

Threshold costs 0.2b (97.5%)

Counts

285 → 1

Compiler

Compiled 63744 to 38592 computations (39.5% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

end104.0ms (1.6%)

Remove: (sort a b c d e)
Compiler: Compiled 187 to 111 computations (40.6% saved)

Details

analyze3.0ms (0%)

sample1.2s (18.7%)

simplify8.0ms (0.1%)

prune2.0ms (0%)

localize9.0ms (0.1%)

series17.0ms (0.3%)

rewrite88.0ms (1.4%)

simplify39.0ms (0.6%)

prune132.0ms (2%)

localize11.0ms (0.2%)

series10.0ms (0.2%)

rewrite54.0ms (0.8%)

simplify23.0ms (0.4%)

prune75.0ms (1.2%)

localize8.0ms (0.1%)

series13.0ms (0.2%)

rewrite79.0ms (1.2%)

simplify97.0ms (1.5%)

prune178.0ms (2.7%)

localize19.0ms (0.3%)

series204.0ms (3.1%)

rewrite95.0ms (1.5%)

simplify99.0ms (1.5%)

prune154.0ms (2.4%)

regimes3.8s (57.8%)

simplify2.0ms (0%)

end104.0ms (1.6%)

Profiling