Details

analyze679.0ms (3.1%)

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
25%	74.9%	0.2%	5
25%	74.9%	0.2%	6
25%	74.9%	0.2%	7
37.4%	62.4%	0.2%	8
56.1%	43.7%	0.2%	9
56.1%	43.7%	0.2%	10
56.1%	43.7%	0.2%	11
65.5%	34.3%	0.2%	12
76.4%	23.4%	0.2%	13
76.4%	23.4%	0.2%	14

Compiler

Compiled 16 to 11 computations (31.3% saved)

sample1.4s (6.3%)

Symmetry

(sort z t)

Results

1.3s

8256×

body

128

valid

Compiler

Compiled 47 to 32 computations (31.9% saved)

simplify194.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

1226×	`div-sub_binary64`
778×	`fma-def_binary64`
701×	`unsub-neg_binary64`
456×	`sub-neg_binary64`
437×	`fma-neg_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	16
1	22	16
2	50	16
3	121	16
4	299	16
5	674	16
6	1361	16
7	2742	16
8	3706	16
9	3871	16
10	4083	16
11	4304	16
12	4387	16
13	5424	16

prune3.0ms (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

0.6b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.6b	(-.f64 1 (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))))

Compiler

Compiled 45 to 30 computations (33.3% saved)

localize9.0ms (0%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 1 (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))))
✓	0.0b	(*.f64 (-.f64 y z) (-.f64 y t))
✓	6.1b	(/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))

series413.0ms (1.9%)

Counts

3 → 132

Calls

3 calls:

225.0ms	(/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))
168.0ms	(-.f64 1 (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))))
19.0ms	(*.f64 (-.f64 y z) (-.f64 y t))

rewrite88.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

63×	`prod-diff_binary64`
54×	`add-sqr-sqrt_binary64`
52×	`*-un-lft-identity_binary64`
45×	`add-cube-cbrt_binary64`
40×	`associate-/r/_binary64`

Counts

3 → 168

Calls

3 calls:

22.0ms	(-.f64 1 (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))))
18.0ms	(*.f64 (-.f64 y z) (-.f64 y t))
14.0ms	(/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))

simplify373.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

787×	`times-frac_binary64`
279×	`fma-def_binary64`
192×	`distribute-rgt-in_binary64`
175×	`distribute-lft-in_binary64`
165×	`sub-neg_binary64`

Counts

300 → 344

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	627	13333
1	1955	11667
2	5135	11667

prune736.0ms (3.3%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	339	5	344
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	340	5	345

Error

Counts

345 → 5

Alt Table

Status	Error	Program
	0.8b	(-.f64 1 (/.f64 (/.f64 x (-.f64 y z)) (-.f64 y t)))
	33.0b	(-.f64 1 (/.f64 (sqrt.f64 x) (/.f64 (*.f64 (-.f64 y z) (-.f64 y t)) (sqrt.f64 x))))
	5.3b	(+.f64 (fma.f64 1 1 (neg.f64 (.f64 (/.f64 x (-.f64 y t)) (/.f64 1 (-.f64 y z))))) (fma.f64 (neg.f64 (/.f64 x (-.f64 y t))) (/.f64 1 (-.f64 y z)) (.f64 (/.f64 x (-.f64 y t)) (/.f64 1 (-.f64 y z)))))
▶	0.5b	(-.f64 1 (.f64 x (/.f64 1 (.f64 (-.f64 y z) (-.f64 y t)))))
	0.6b	(-.f64 1 (/.f64 1 (/.f64 (*.f64 (-.f64 y z) (-.f64 y t)) x)))

Compiler

Compiled 14004 to 5026 computations (64.1% saved)

localize8.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 1 (.f64 x (/.f64 1 (.f64 (-.f64 y z) (-.f64 y t)))))
	0.0b	(*.f64 (-.f64 y z) (-.f64 y t))
✓	0.4b	(/.f64 1 (*.f64 (-.f64 y z) (-.f64 y t)))
✓	5.9b	(.f64 x (/.f64 1 (.f64 (-.f64 y z) (-.f64 y t))))

series565.0ms (2.5%)

Counts

3 → 132

Calls

3 calls:

223.0ms	(-.f64 1 (.f64 x (/.f64 1 (.f64 (-.f64 y z) (-.f64 y t)))))
209.0ms	(.f64 x (/.f64 1 (.f64 (-.f64 y z) (-.f64 y t))))
132.0ms	(/.f64 1 (*.f64 (-.f64 y z) (-.f64 y t)))

rewrite53.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

33×	`add-exp-log_binary64`
17×	`add-cbrt-cube_binary64`
16×	`associate-/r/_binary64`
15×	`associate-r_binary64`
13×	`flip--_binary64`

Counts

3 → 100

Calls

3 calls:

23.0ms	(.f64 x (/.f64 1 (.f64 (-.f64 y z) (-.f64 y t))))
13.0ms	(/.f64 1 (*.f64 (-.f64 y z) (-.f64 y t)))
5.0ms	(-.f64 1 (.f64 x (/.f64 1 (.f64 (-.f64 y z) (-.f64 y t)))))

simplify310.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

826×	`associate-/r*_binary64`
816×	`associate-/l*_binary64`
266×	`fma-def_binary64`
196×	`+-commutative_binary64`
159×	`sub-neg_binary64`

Counts

232 → 288

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	632	11312
1	2138	10842
2	5817	10842

prune764.0ms (3.4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	379	0	379
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	379	5	384

Error

Counts

384 → 5

Alt Table

Status	Error	Program
	0.8b	(-.f64 1 (/.f64 (/.f64 x (-.f64 y z)) (-.f64 y t)))
	33.0b	(-.f64 1 (/.f64 (sqrt.f64 x) (/.f64 (*.f64 (-.f64 y z) (-.f64 y t)) (sqrt.f64 x))))
	5.3b	(+.f64 (fma.f64 1 1 (neg.f64 (.f64 (/.f64 x (-.f64 y t)) (/.f64 1 (-.f64 y z))))) (fma.f64 (neg.f64 (/.f64 x (-.f64 y t))) (/.f64 1 (-.f64 y z)) (.f64 (/.f64 x (-.f64 y t)) (/.f64 1 (-.f64 y z)))))
✓	0.5b	(-.f64 1 (.f64 x (/.f64 1 (.f64 (-.f64 y z) (-.f64 y t)))))
▶	0.6b	(-.f64 1 (/.f64 1 (/.f64 (*.f64 (-.f64 y z) (-.f64 y t)) x)))

Compiler

Compiled 14361 to 6525 computations (54.6% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 1 (/.f64 1 (/.f64 (*.f64 (-.f64 y z) (-.f64 y t)) x)))
	0.0b	(*.f64 (-.f64 y z) (-.f64 y t))
✓	0.5b	(/.f64 1 (/.f64 (*.f64 (-.f64 y z) (-.f64 y t)) x))
✓	5.8b	(/.f64 (*.f64 (-.f64 y z) (-.f64 y t)) x)

series522.0ms (2.3%)

Counts

3 → 144

Calls

3 calls:

269.0ms	(/.f64 1 (/.f64 (*.f64 (-.f64 y z) (-.f64 y t)) x))
195.0ms	(-.f64 1 (/.f64 1 (/.f64 (*.f64 (-.f64 y z) (-.f64 y t)) x)))
57.0ms	(/.f64 (*.f64 (-.f64 y z) (-.f64 y t)) x)

rewrite98.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

160×	`times-frac_binary64`
115×	`add-sqr-sqrt_binary64`
112×	`*-un-lft-identity_binary64`
104×	`add-cube-cbrt_binary64`
78×	`prod-diff_binary64`

Counts

3 → 217

Calls

3 calls:

24.0ms	(-.f64 1 (/.f64 1 (/.f64 (*.f64 (-.f64 y z) (-.f64 y t)) x)))
17.0ms	(/.f64 (*.f64 (-.f64 y z) (-.f64 y t)) x)
15.0ms	(/.f64 1 (/.f64 (*.f64 (-.f64 y z) (-.f64 y t)) x))

simplify343.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

788×	`times-frac_binary64`
618×	`associate-/l*_binary64`
246×	`fma-def_binary64`
172×	`associate-/r/_binary64`
159×	`sub-neg_binary64`

Counts

361 → 390

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	546	16926
1	1780	14143
2	5334	14143

prune820.0ms (3.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	480	1	481
Fresh	1	2	3
Picked	0	1	1
Done	1	0	1
Total	482	4	486

Error

Counts

486 → 4

Alt Table

Status	Error	Program
▶	0.6b	(-.f64 1 (/.f64 (/.f64 1 (*.f64 (-.f64 y z) (-.f64 y t))) (/.f64 1 x)))
	0.8b	(-.f64 1 (/.f64 (/.f64 x (-.f64 y z)) (-.f64 y t)))
	5.3b	(+.f64 (fma.f64 1 1 (neg.f64 (.f64 (/.f64 x (-.f64 y t)) (/.f64 1 (-.f64 y z))))) (fma.f64 (neg.f64 (/.f64 x (-.f64 y t))) (/.f64 1 (-.f64 y z)) (.f64 (/.f64 x (-.f64 y t)) (/.f64 1 (-.f64 y z)))))
✓	0.6b	(-.f64 1 (/.f64 1 (/.f64 (*.f64 (-.f64 y z) (-.f64 y t)) x)))

Compiler

Compiled 18704 to 7727 computations (58.7% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 1 (/.f64 (/.f64 1 (*.f64 (-.f64 y z) (-.f64 y t))) (/.f64 1 x)))
	0.0b	(*.f64 (-.f64 y z) (-.f64 y t))
	0.4b	(/.f64 1 (*.f64 (-.f64 y z) (-.f64 y t)))
✓	6.0b	(/.f64 (/.f64 1 (*.f64 (-.f64 y z) (-.f64 y t))) (/.f64 1 x))

series431.0ms (1.9%)

Counts

2 → 96

Calls

2 calls:

267.0ms	(/.f64 (/.f64 1 (*.f64 (-.f64 y z) (-.f64 y t))) (/.f64 1 x))
163.0ms	(-.f64 1 (/.f64 (/.f64 1 (*.f64 (-.f64 y z) (-.f64 y t))) (/.f64 1 x)))

rewrite701.0ms (3.2%)

Algorithm

1×	rewrite-expression-head

Rules

1867×	`times-frac_binary64`
891×	`add-sqr-sqrt_binary64`
879×	`*-un-lft-identity_binary64`
871×	`add-cube-cbrt_binary64`
600×	`prod-diff_binary64`

Counts

2 → 1096

Calls

2 calls:

130.0ms	(-.f64 1 (/.f64 (/.f64 1 (*.f64 (-.f64 y z) (-.f64 y t))) (/.f64 1 x)))
32.0ms	(/.f64 (/.f64 1 (*.f64 (-.f64 y z) (-.f64 y t))) (/.f64 1 x))

simplify3.7s (16.8%)

Algorithm

1×	egg-herbie

Rules

763×	`times-frac_binary64`
398×	`fma-def_binary64`
225×	`*-commutative_binary64`
192×	`neg-mul-1_binary64`
188×	`neg-sub0_binary64`

Counts

1192 → 1276

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1052	100064
1	3534	99123
2	4990	99123

prune4.6s (20.8%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	1462	0	1462
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	1462	4	1466

Error

Counts

1466 → 4

Alt Table

Status	Error	Program
✓	0.6b	(-.f64 1 (/.f64 (/.f64 1 (*.f64 (-.f64 y z) (-.f64 y t))) (/.f64 1 x)))
	0.8b	(-.f64 1 (/.f64 (/.f64 x (-.f64 y z)) (-.f64 y t)))
	5.3b	(+.f64 (fma.f64 1 1 (neg.f64 (.f64 (/.f64 x (-.f64 y t)) (/.f64 1 (-.f64 y z))))) (fma.f64 (neg.f64 (/.f64 x (-.f64 y t))) (/.f64 1 (-.f64 y z)) (.f64 (/.f64 x (-.f64 y t)) (/.f64 1 (-.f64 y z)))))
✓	0.6b	(-.f64 1 (/.f64 1 (/.f64 (*.f64 (-.f64 y z) (-.f64 y t)) x)))

Compiler

Compiled 96722 to 47213 computations (51.2% saved)

regimes5.0s (22.3%)

Accuracy

Total 0.6b remaining (98.4%)

Threshold costs 0.6b (98.4%)

Counts

317 → 1

Compiler

Compiled 63236 to 42766 computations (32.4% saved)

simplify6.0ms (0%)

Algorithm

1×	egg-herbie

Rules

5×	`+-commutative_binary64`
4×	`sub-neg_binary64`
3×	`*-commutative_binary64`
2×	`neg-sub0_binary64`
2×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	31
1	24	31
2	30	31
3	34	31
4	36	31
5	35	31

end370.0ms (1.7%)

Compiler: Compiled 190 to 118 computations (37.9% saved)

Details

analyze679.0ms (3.1%)

sample1.4s (6.3%)

simplify194.0ms (0.9%)

prune3.0ms (0%)

localize9.0ms (0%)

series413.0ms (1.9%)

rewrite88.0ms (0.4%)

simplify373.0ms (1.7%)

prune736.0ms (3.3%)

localize8.0ms (0%)

series565.0ms (2.5%)

rewrite53.0ms (0.2%)

simplify310.0ms (1.4%)

prune764.0ms (3.4%)

localize17.0ms (0.1%)

series522.0ms (2.3%)

rewrite98.0ms (0.4%)

simplify343.0ms (1.5%)

prune820.0ms (3.7%)

localize19.0ms (0.1%)

series431.0ms (1.9%)

rewrite701.0ms (3.2%)

simplify3.7s (16.8%)

prune4.6s (20.8%)

regimes5.0s (22.3%)

simplify6.0ms (0%)

end370.0ms (1.7%)

Profiling