Details

analyze1.1s (24.6%)

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
9.4%	90.4%	0.2%	10
22.2%	77.6%	0.2%	11
40.4%	59.5%	0.2%	12
47.4%	52.4%	0.2%	13
55.3%	44.5%	0.2%	14

Compiler

Compiled 22 to 15 computations (31.8% saved)

sample1.2s (27%)

Results

1.2s

8256×

body

128

valid

Compiler

Compiled 65 to 44 computations (32.3% saved)

simplify54.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

508×	`fma-neg_binary64`
504×	`associate-*l/_binary64`
466×	`div-sub_binary64`
450×	`cancel-sign-sub-inv_binary64`
403×	`sub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	14	25
1	30	25
2	70	25
3	177	22
4	486	19
5	1087	19
6	2534	19
7	4434	19
8	5156	19

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

2.2b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	2.7b	(-.f64 x (/.f64 y (-.f64 z (/.f64 (.f64 y t) (.f64 2 z)))))
	12.7b	(-.f64 x (/.f64 (.f64 (.f64 y 2) z) (-.f64 (.f64 (.f64 z 2) z) (*.f64 y t))))

Compiler

Compiled 110 to 70 computations (36.4% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 x (/.f64 y (-.f64 z (/.f64 (.f64 y t) (.f64 2 z)))))
✓	5.4b	(/.f64 (.f64 y t) (.f64 2 z))
✓	6.3b	(/.f64 y (-.f64 z (/.f64 (.f64 y t) (.f64 2 z))))

series79.0ms (1.7%)

Counts

3 → 120

Calls

3 calls:

38.0ms	(-.f64 x (/.f64 y (-.f64 z (/.f64 (.f64 y t) (.f64 2 z)))))
26.0ms	(/.f64 y (-.f64 z (/.f64 (.f64 y t) (.f64 2 z))))
14.0ms	(/.f64 (.f64 y t) (.f64 2 z))

rewrite113.0ms (2.5%)

Algorithm

2×	batch-egg-rewrite

Rules

267×	`expm1-udef_binary64`
267×	`log1p-udef_binary64`
146×	`add-sqr-sqrt_binary64`
140×	`log1p-expm1-u_binary64`
140×	`expm1-log1p-u_binary64`

Counts

3 → 125

Calls

3 calls:

110.0ms	(-.f64 x (/.f64 y (-.f64 z (/.f64 (.f64 y t) (.f64 2 z)))))
110.0ms	(/.f64 (.f64 y t) (.f64 2 z))
110.0ms	(/.f64 y (-.f64 z (/.f64 (.f64 y t) (.f64 2 z))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	45
1	279	45
2	4155	45
3	4989	45
4	4939	45
0	0	0
1	0	0

simplify88.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

621×	`fma-neg_binary64`
529×	`times-frac_binary64`
345×	`associate-/l*_binary64`
300×	`associate-/r*_binary64`
245×	`associate-r_binary64`

Counts

245 → 164

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	91	2594
1	273	2584
2	899	2544
3	4272	2534
4	4957	2534

prune134.0ms (2.9%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	160	4	164
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	162	4	166

Error

Counts

166 → 4

Alt Table

Status	Error	Program
	24.3b	(fma.f64 2 (/.f64 z t) x)
▶	0.8b	(-.f64 x (/.f64 y (-.f64 z (*.f64 (/.f64 y 2) (/.f64 t z)))))
	3.0b	(-.f64 x (pow.f64 (cbrt.f64 (/.f64 y (-.f64 z (/.f64 (.f64 y t) (.f64 z 2))))) 3))
	2.7b	(-.f64 x (.f64 y (/.f64 1 (-.f64 z (/.f64 (.f64 y t) (*.f64 z 2))))))

Compiler

Compiled 3730 to 2057 computations (44.9% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 x (/.f64 y (-.f64 z (*.f64 (/.f64 y 2) (/.f64 t z)))))
✓	6.0b	(*.f64 (/.f64 y 2) (/.f64 t z))
✓	6.3b	(/.f64 y (-.f64 z (*.f64 (/.f64 y 2) (/.f64 t z))))

series78.0ms (1.7%)

Counts

3 → 120

Calls

3 calls:

37.0ms	(-.f64 x (/.f64 y (-.f64 z (*.f64 (/.f64 y 2) (/.f64 t z)))))
27.0ms	(/.f64 y (-.f64 z (*.f64 (/.f64 y 2) (/.f64 t z))))
13.0ms	(*.f64 (/.f64 y 2) (/.f64 t z))

rewrite85.0ms (1.9%)

Algorithm

2×	batch-egg-rewrite

Rules

273×	`expm1-udef_binary64`
273×	`log1p-udef_binary64`
151×	`add-sqr-sqrt_binary64`
145×	`log1p-expm1-u_binary64`
145×	`expm1-log1p-u_binary64`

Counts

3 → 121

Calls

3 calls:

82.0ms	(-.f64 x (/.f64 y (-.f64 z (*.f64 (/.f64 y 2) (/.f64 t z)))))
82.0ms	(*.f64 (/.f64 y 2) (/.f64 t z))
82.0ms	(/.f64 y (-.f64 z (*.f64 (/.f64 y 2) (/.f64 t z))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	45
1	289	45
2	4215	45
3	4970	45
0	0	0
1	0	0

simplify85.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

621×	`fma-neg_binary64`
529×	`times-frac_binary64`
345×	`associate-/l*_binary64`
300×	`associate-/r*_binary64`
245×	`associate-r_binary64`

Counts

241 → 161

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	91	2594
1	273	2584
2	899	2544
3	4272	2534
4	4957	2534

prune118.0ms (2.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	161	0	161
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	161	4	165

Error

Counts

165 → 4

Alt Table

Status	Error	Program
	24.3b	(fma.f64 2 (/.f64 z t) x)
✓	0.8b	(-.f64 x (/.f64 y (-.f64 z (*.f64 (/.f64 y 2) (/.f64 t z)))))
	3.0b	(-.f64 x (pow.f64 (cbrt.f64 (/.f64 y (-.f64 z (/.f64 (.f64 y t) (.f64 z 2))))) 3))
▶	2.7b	(-.f64 x (.f64 y (/.f64 1 (-.f64 z (/.f64 (.f64 y t) (*.f64 z 2))))))

Compiler

Compiled 3538 to 1939 computations (45.2% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 x (.f64 y (/.f64 1 (-.f64 z (/.f64 (.f64 y t) (*.f64 z 2))))))
✓	0.5b	(/.f64 1 (-.f64 z (/.f64 (.f64 y t) (.f64 z 2))))
✓	5.4b	(/.f64 (.f64 y t) (.f64 z 2))
✓	5.9b	(.f64 y (/.f64 1 (-.f64 z (/.f64 (.f64 y t) (*.f64 z 2)))))

series96.0ms (2.1%)

Counts

4 → 156

Calls

4 calls:

38.0ms	(-.f64 x (.f64 y (/.f64 1 (-.f64 z (/.f64 (.f64 y t) (*.f64 z 2))))))
23.0ms	(.f64 y (/.f64 1 (-.f64 z (/.f64 (.f64 y t) (*.f64 z 2)))))
21.0ms	(/.f64 1 (-.f64 z (/.f64 (.f64 y t) (.f64 z 2))))
14.0ms	(/.f64 (.f64 y t) (.f64 z 2))

rewrite95.0ms (2.1%)

Algorithm

2×	batch-egg-rewrite

Rules

285×	`expm1-udef_binary64`
285×	`log1p-udef_binary64`
161×	`add-sqr-sqrt_binary64`
154×	`log1p-expm1-u_binary64`
154×	`expm1-log1p-u_binary64`

Counts

4 → 139

Calls

4 calls:

92.0ms	(-.f64 x (.f64 y (/.f64 1 (-.f64 z (/.f64 (.f64 y t) (*.f64 z 2))))))
92.0ms	(/.f64 1 (-.f64 z (/.f64 (.f64 y t) (.f64 z 2))))
92.0ms	(/.f64 (.f64 y t) (.f64 z 2))
92.0ms	(.f64 y (/.f64 1 (-.f64 z (/.f64 (.f64 y t) (*.f64 z 2)))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	61
1	318	61
2	4413	61
3	5204	61
0	0	0
1	0	0

simplify94.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

608×	`associate-/l*_binary64`
552×	`associate-/r*_binary64`
389×	`fma-def_binary64`
342×	`associate-l_binary64`
224×	`associate-*l/_binary64`

Counts

295 → 192

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	122	3842
1	373	3832
2	1344	3772
3	5104	3772

prune153.0ms (3.4%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	192	0	192
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	192	4	196

Error

Counts

196 → 4

Alt Table

Status	Error	Program
	24.3b	(fma.f64 2 (/.f64 z t) x)
✓	0.8b	(-.f64 x (/.f64 y (-.f64 z (*.f64 (/.f64 y 2) (/.f64 t z)))))
▶	3.0b	(-.f64 x (pow.f64 (cbrt.f64 (/.f64 y (-.f64 z (/.f64 (.f64 y t) (.f64 z 2))))) 3))
✓	2.7b	(-.f64 x (.f64 y (/.f64 1 (-.f64 z (/.f64 (.f64 y t) (*.f64 z 2))))))

Compiler

Compiled 4483 to 2567 computations (42.7% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(pow.f64 (cbrt.f64 (/.f64 y (-.f64 z (/.f64 (.f64 y t) (.f64 z 2))))) 3)
	5.4b	(/.f64 (.f64 y t) (.f64 z 2))
✓	6.3b	(/.f64 y (-.f64 z (/.f64 (.f64 y t) (.f64 z 2))))
✓	13.8b	(cbrt.f64 (/.f64 y (-.f64 z (/.f64 (.f64 y t) (.f64 z 2)))))

series226.0ms (5%)

Counts

3 → 108

Calls

3 calls:

136.0ms	(pow.f64 (cbrt.f64 (/.f64 y (-.f64 z (/.f64 (.f64 y t) (.f64 z 2))))) 3)
66.0ms	(cbrt.f64 (/.f64 y (-.f64 z (/.f64 (.f64 y t) (.f64 z 2)))))
23.0ms	(/.f64 y (-.f64 z (/.f64 (.f64 y t) (.f64 z 2))))

rewrite77.0ms (1.7%)

Algorithm

2×	batch-egg-rewrite

Rules

767×	`prod-diff_binary64`
135×	`add-sqr-sqrt_binary64`
132×	`log1p-expm1-u_binary64`
132×	`expm1-log1p-u_binary64`
128×	`add-log-exp_binary64`

Counts

3 → 121

Calls

3 calls:

74.0ms	(pow.f64 (cbrt.f64 (/.f64 y (-.f64 z (/.f64 (.f64 y t) (.f64 z 2))))) 3)
74.0ms	(/.f64 y (-.f64 z (/.f64 (.f64 y t) (.f64 z 2))))
74.0ms	(cbrt.f64 (/.f64 y (-.f64 z (/.f64 (.f64 y t) (.f64 z 2)))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	50
1	276	50
2	3822	50
3	5398	50
0	0	0
1	0	0

simplify94.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

401×	`associate-r_binary64`
381×	`times-frac_binary64`
376×	`fma-def_binary64`
319×	`associate-/l*_binary64`
292×	`associate-/r*_binary64`

Counts

229 → 222

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	403	5911
1	1321	5715
2	5114	5715

prune265.0ms (5.8%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	276	0	276
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	276	4	280

Error

Counts

280 → 4

Alt Table

Status	Error	Program
	24.3b	(fma.f64 2 (/.f64 z t) x)
✓	0.8b	(-.f64 x (/.f64 y (-.f64 z (*.f64 (/.f64 y 2) (/.f64 t z)))))
✓	3.0b	(-.f64 x (pow.f64 (cbrt.f64 (/.f64 y (-.f64 z (/.f64 (.f64 y t) (.f64 z 2))))) 3))
✓	2.7b	(-.f64 x (.f64 y (/.f64 1 (-.f64 z (/.f64 (.f64 y t) (*.f64 z 2))))))

Compiler

Compiled 9564 to 6398 computations (33.1% saved)

regimes153.0ms (3.4%)

Accuracy

Total 1.1b remaining (99.5%)

Threshold costs 0b (0%)

Counts

23 → 1

Compiler

Compiled 2452 to 1666 computations (32.1% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

8×	`+-commutative_binary64`
8×	`sub-neg_binary64`
7×	`*-commutative_binary64`
6×	`neg-sub0_binary64`
6×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	19
1	20	19
2	36	19
3	48	19
4	57	19
5	61	19
6	62	19
7	62	19

end67.0ms (1.5%)

Compiler: Compiled 100 to 67 computations (33% saved)

Details

analyze1.1s (24.6%)

sample1.2s (27%)

simplify54.0ms (1.2%)

prune4.0ms (0.1%)

localize8.0ms (0.2%)

series79.0ms (1.7%)

rewrite113.0ms (2.5%)

simplify88.0ms (1.9%)

prune134.0ms (2.9%)

localize8.0ms (0.2%)

series78.0ms (1.7%)

rewrite85.0ms (1.9%)

simplify85.0ms (1.9%)

prune118.0ms (2.6%)

localize11.0ms (0.2%)

series96.0ms (2.1%)

rewrite95.0ms (2.1%)

simplify94.0ms (2.1%)

prune153.0ms (3.4%)

localize11.0ms (0.2%)

series226.0ms (5%)

rewrite77.0ms (1.7%)

simplify94.0ms (2.1%)

prune265.0ms (5.8%)

regimes153.0ms (3.4%)

simplify3.0ms (0.1%)

end67.0ms (1.5%)

Profiling