Details

analyze992.0ms (26.6%)

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
9.4%	90.4%	0.2%	8
9.4%	90.4%	0.2%	9
10.9%	88.9%	0.2%	10
25.9%	73.9%	0.2%	11
47.1%	52.7%	0.2%	12
55.3%	44.5%	0.2%	13
59.2%	40.6%	0.2%	14

Compiler

Compiled 22 to 15 computations (31.8% saved)

sample24.0ms (0.7%)

Algorithm

1×

intervals

Results

14.0ms

256×

body

128

valid

Compiler

Compiled 47 to 33 computations (29.8% saved)

simplify56.0ms (1.5%)

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)))))
	11.6b	(-.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)))))
✓	3.8b	(/.f64 (.f64 y t) (.f64 2 z))
✓	6.8b	(/.f64 y (-.f64 z (/.f64 (.f64 y t) (.f64 2 z))))

series93.0ms (2.5%)

Counts

3 → 120

Calls

3 calls:

46.0ms	(-.f64 x (/.f64 y (-.f64 z (/.f64 (.f64 y t) (.f64 2 z)))))
32.0ms	(/.f64 y (-.f64 z (/.f64 (.f64 y t) (.f64 2 z))))
15.0ms	(/.f64 (.f64 y t) (.f64 2 z))

rewrite48.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

108×	`add-sqr-sqrt_binary64`
105×	`*-un-lft-identity_binary64`
77×	`times-frac_binary64`
71×	`add-cube-cbrt_binary64`
63×	`prod-diff_binary64`

Counts

3 → 165

Calls

3 calls:

11.0ms	(-.f64 x (/.f64 y (-.f64 z (/.f64 (.f64 y t) (.f64 2 z)))))
5.0ms	(/.f64 y (-.f64 z (/.f64 (.f64 y t) (.f64 2 z))))
4.0ms	(/.f64 (.f64 y t) (.f64 2 z))

simplify180.0ms (4.8%)

Algorithm

1×	egg-herbie

Rules

325×	`cancel-sign-sub-inv_binary64`
304×	`distribute-neg-frac_binary64`
221×	`times-frac_binary64`
203×	`associate-/l*_binary64`
182×	`associate-*r/_binary64`

Counts

285 → 254

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	384	10579
1	1057	7887
2	3351	6717
3	4786	6717

prune247.0ms (6.6%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	251	3	254
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	253	3	256

Error

Counts

256 → 3

Alt Table

Status	Error	Program
▶	1.5b	(-.f64 x (/.f64 y (-.f64 z (*.f64 (/.f64 y 2) (/.f64 t z)))))
	2.7b	(-.f64 x (.f64 y (/.f64 1 (-.f64 z (/.f64 (.f64 y t) (*.f64 2 z))))))
	24.5b	(fma.f64 2 (/.f64 z t) x)

Compiler

Compiled 9913 to 5045 computations (49.1% 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)))))
✓	5.5b	(*.f64 (/.f64 y 2) (/.f64 t z))
✓	6.8b	(/.f64 y (-.f64 z (*.f64 (/.f64 y 2) (/.f64 t z))))

series101.0ms (2.7%)

Counts

3 → 120

Calls

3 calls:

45.0ms	(-.f64 x (/.f64 y (-.f64 z (*.f64 (/.f64 y 2) (/.f64 t z)))))
31.0ms	(/.f64 y (-.f64 z (*.f64 (/.f64 y 2) (/.f64 t z))))
25.0ms	(*.f64 (/.f64 y 2) (/.f64 t z))

rewrite42.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

86×	`add-sqr-sqrt_binary64`
71×	`*-un-lft-identity_binary64`
69×	`add-cube-cbrt_binary64`
68×	`times-frac_binary64`
45×	`prod-diff_binary64`

Counts

3 → 162

Calls

3 calls:

8.0ms	(-.f64 x (/.f64 y (-.f64 z (*.f64 (/.f64 y 2) (/.f64 t z)))))
8.0ms	(*.f64 (/.f64 y 2) (/.f64 t z))
6.0ms	(/.f64 y (-.f64 z (*.f64 (/.f64 y 2) (/.f64 t z))))

simplify213.0ms (5.7%)

Algorithm

1×	egg-herbie

Rules

898×	`fma-def_binary64`
241×	`associate-*r/_binary64`
221×	`associate-*l/_binary64`
198×	`fma-neg_binary64`
193×	`*-commutative_binary64`

Counts

282 → 245

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	399	9065
1	1098	7039
2	3324	6174
3	4775	6174
4	4814	6174

prune185.0ms (5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	245	0	245
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	245	3	248

Error

Counts

248 → 3

Alt Table

Status	Error	Program
✓	1.5b	(-.f64 x (/.f64 y (-.f64 z (*.f64 (/.f64 y 2) (/.f64 t z)))))
▶	2.7b	(-.f64 x (.f64 y (/.f64 1 (-.f64 z (/.f64 (.f64 y t) (*.f64 2 z))))))
	24.5b	(fma.f64 2 (/.f64 z t) x)

Compiler

Compiled 8840 to 4532 computations (48.7% saved)

localize9.0ms (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 2 z))))))
✓	0.4b	(/.f64 1 (-.f64 z (/.f64 (.f64 y t) (.f64 2 z))))
	3.8b	(/.f64 (.f64 y t) (.f64 2 z))
✓	6.7b	(.f64 y (/.f64 1 (-.f64 z (/.f64 (.f64 y t) (*.f64 2 z)))))

series102.0ms (2.7%)

Counts

3 → 120

Calls

3 calls:

44.0ms	(-.f64 x (.f64 y (/.f64 1 (-.f64 z (/.f64 (.f64 y t) (*.f64 2 z))))))
30.0ms	(.f64 y (/.f64 1 (-.f64 z (/.f64 (.f64 y t) (*.f64 2 z)))))
27.0ms	(/.f64 1 (-.f64 z (/.f64 (.f64 y t) (.f64 2 z))))

rewrite26.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

46×	`add-sqr-sqrt_binary64`
40×	`*-un-lft-identity_binary64`
32×	`times-frac_binary64`
25×	`add-cube-cbrt_binary64`
21×	`associate-r_binary64`

Counts

3 → 109

Calls

3 calls:

10.0ms	(.f64 y (/.f64 1 (-.f64 z (/.f64 (.f64 y t) (*.f64 2 z)))))
5.0ms	(/.f64 1 (-.f64 z (/.f64 (.f64 y t) (.f64 2 z))))
3.0ms	(-.f64 x (.f64 y (/.f64 1 (-.f64 z (/.f64 (.f64 y t) (*.f64 2 z))))))

simplify152.0ms (4.1%)

Algorithm

1×	egg-herbie

Rules

635×	`fma-def_binary64`
234×	`fma-neg_binary64`
231×	`associate-/r/_binary64`
206×	`associate-/l/_binary64`
205×	`distribute-rgt-neg-in_binary64`

Counts

229 → 213

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	235	6000
1	624	5773
2	2130	5441
3	4879	5441
4	4927	5441

prune185.0ms (5%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	250	0	250
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	250	3	253

Error

Counts

253 → 3

Alt Table

Status	Error	Program
✓	1.5b	(-.f64 x (/.f64 y (-.f64 z (*.f64 (/.f64 y 2) (/.f64 t z)))))
✓	2.7b	(-.f64 x (.f64 y (/.f64 1 (-.f64 z (/.f64 (.f64 y t) (*.f64 2 z))))))
▶	24.5b	(fma.f64 2 (/.f64 z t) x)

Compiler

Compiled 6395 to 3517 computations (45% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 2 (/.f64 z t) x)

series9.0ms (0.3%)

Counts

1 → 36

Calls

1 calls:

9.0ms

(fma.f64 2 (/.f64 z t) x)

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

1×	`*-un-lft-identity_binary64`
1×	`add-sqr-sqrt_binary64`
1×	`add-cube-cbrt_binary64`
1×	`add-cbrt-cube_binary64`
1×	`add-exp-log_binary64`

Counts

1 → 10

Calls

1 calls:

0.0ms

(fma.f64 2 (/.f64 z t) x)

simplify83.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

548×	`associate-*l/_binary64`
542×	`distribute-rgt-in_binary64`
507×	`distribute-lft-in_binary64`
443×	`associate-+l+_binary64`
396×	`fma-def_binary64`

Counts

46 → 14

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	18	376
1	23	359
2	49	359
3	126	359
4	432	359
5	1628	359
6	4283	359
7	4686	359
8	4929	359
9	4999	359

prune7.0ms (0.2%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	14	0	14
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	14	3	17

Error

Counts

17 → 3

Alt Table

Status	Error	Program
✓	1.5b	(-.f64 x (/.f64 y (-.f64 z (*.f64 (/.f64 y 2) (/.f64 t z)))))
✓	2.7b	(-.f64 x (.f64 y (/.f64 1 (-.f64 z (/.f64 (.f64 y t) (*.f64 2 z))))))
✓	24.5b	(fma.f64 2 (/.f64 z t) x)

Compiler

Compiled 185 to 99 computations (46.5% saved)

regimes122.0ms (3.3%)

Accuracy

Total 1.1b remaining (99.4%)

Threshold costs 0b (0%)

Counts

19 → 1

Compiler

Compiled 1954 to 1306 computations (33.2% saved)

simplify4.0ms (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

end0.0ms (0%)

Compiler: Compiled 17 to 11 computations (35.3% saved)

sample815.0ms (21.9%)

Algorithm

1×

intervals

Results

487.0ms

8000×

body

128

valid

Compiler

Compiled 89 to 61 computations (31.5% saved)

Details

analyze992.0ms (26.6%)

sample24.0ms (0.7%)

simplify56.0ms (1.5%)

prune4.0ms (0.1%)

localize8.0ms (0.2%)

series93.0ms (2.5%)

rewrite48.0ms (1.3%)

simplify180.0ms (4.8%)

prune247.0ms (6.6%)

localize8.0ms (0.2%)

series101.0ms (2.7%)

rewrite42.0ms (1.1%)

simplify213.0ms (5.7%)

prune185.0ms (5%)

localize9.0ms (0.2%)

series102.0ms (2.7%)

rewrite26.0ms (0.7%)

simplify152.0ms (4.1%)

prune185.0ms (5%)

localize4.0ms (0.1%)

series9.0ms (0.3%)

rewrite1.0ms (0%)

simplify83.0ms (2.2%)

prune7.0ms (0.2%)

regimes122.0ms (3.3%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample815.0ms (21.9%)

Profiling