Details

analyze1.9s (31.4%)

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
0%	99.8%	0.2%	8
6.2%	93.6%	0.2%	9
12.5%	87.3%	0.2%	10
15.6%	80.3%	4.1%	11
31.2%	63.9%	4.9%	12
39%	50.9%	10.1%	13
44.8%	44.4%	10.7%	14

Compiler

Compiled 12 to 8 computations (33.3% saved)

sample59.0ms (1%)

Algorithm

1×

intervals

Results

13.0ms	256×	body	128	valid
2.0ms	45×	body	128	invalid

Compiler

Compiled 27 to 19 computations (29.6% saved)

simplify27.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

171×	`fma-def_binary64`
87×	`fma-neg_binary64`
36×	`cancel-sign-sub-inv_binary64`
23×	`distribute-rgt-neg-in_binary64`
20×	`sub-neg_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	10
1	16	10
2	27	10
3	44	10
4	66	10
5	100	10
6	152	10
7	213	10
8	257	10
9	279	10
10	299	10
11	305	10
12	274	10

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

0.0b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.0b	(-.f64 (.f64 x y) (.f64 z t))

Compiler

Compiled 33 to 21 computations (36.4% saved)

localize10.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (.f64 x y) (.f64 z t))

series21.0ms (0.3%)

Counts

1 → 48

Calls

1 calls:

21.0ms

(-.f64 (*.f64 x y) (*.f64 z t))

rewrite6.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`add-log-exp_binary64`
1×	`cancel-sign-sub-inv_binary64`
1×	`flip--_binary64`
1×	`sub-neg_binary64`
1×	`*-un-lft-identity_binary64`

Counts

1 → 16

Calls

1 calls:

5.0ms

(-.f64 (*.f64 x y) (*.f64 z t))

simplify162.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

480×	`times-frac_binary64`
463×	`fma-def_binary64`
444×	`unsub-neg_binary64`
265×	`sub-neg_binary64`
232×	`distribute-rgt-neg-in_binary64`

Counts

64 → 32

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	43	682
1	113	658
2	347	652
3	974	652
4	2183	652
5	3451	652
6	4489	652
7	4961	652
8	4995	652
9	4859	652

prune35.0ms (0.6%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	30	2	32
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	31	2	33

Error

0.0b

Counts

33 → 2

Alt Table

Status	Error	Program
	31.4b	(.f64 (sqrt.f64 (-.f64 (.f64 x y) (.f64 z t))) (sqrt.f64 (-.f64 (.f64 x y) (*.f64 z t))))
▶	0.0b	(fma.f64 x y (neg.f64 (*.f64 z t)))

Compiler

Compiled 477 to 125 computations (73.8% saved)

localize10.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x y (neg.f64 (*.f64 z t)))

series19.0ms (0.3%)

Counts

1 → 48

Calls

1 calls:

19.0ms

(fma.f64 x y (neg.f64 (*.f64 z t)))

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:

1.0ms

(fma.f64 x y (neg.f64 (*.f64 z t)))

simplify130.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

967×	`unsub-neg_binary64`
792×	`times-frac_binary64`
421×	`fma-neg_binary64`
384×	`neg-sub0_binary64`
364×	`neg-mul-1_binary64`

Counts

58 → 22

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	23	568
1	37	547
2	65	547
3	215	547
4	895	547
5	1760	547
6	3723	547
7	4512	547
8	5729	547

prune16.0ms (0.3%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	22	0	22
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	22	2	24

Error

0.0b

Counts

24 → 2

Alt Table

Status	Error	Program
▶	31.4b	(.f64 (sqrt.f64 (-.f64 (.f64 x y) (.f64 z t))) (sqrt.f64 (-.f64 (.f64 x y) (*.f64 z t))))
✓	0.0b	(fma.f64 x y (neg.f64 (*.f64 z t)))

Compiler

Compiled 302 to 77 computations (74.5% saved)

localize13.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(-.f64 (.f64 x y) (.f64 z t))
✓	0.2b	(.f64 (sqrt.f64 (-.f64 (.f64 x y) (.f64 z t))) (sqrt.f64 (-.f64 (.f64 x y) (*.f64 z t))))
✓	1.8b	(sqrt.f64 (-.f64 (.f64 x y) (.f64 z t)))

series216.0ms (3.5%)

Counts

2 → 56

Calls

2 calls:

129.0ms	(sqrt.f64 (-.f64 (.f64 x y) (.f64 z t)))
87.0ms	(.f64 (sqrt.f64 (-.f64 (.f64 x y) (.f64 z t))) (sqrt.f64 (-.f64 (.f64 x y) (*.f64 z t))))

rewrite46.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`add-sqr-sqrt_binary64`
21×	`sqrt-prod_binary64`
18×	`pow1_binary64`
14×	`sqrt-div_binary64`
11×	`*-un-lft-identity_binary64`

Counts

2 → 78

Calls

2 calls:

24.0ms	(.f64 (sqrt.f64 (-.f64 (.f64 x y) (.f64 z t))) (sqrt.f64 (-.f64 (.f64 x y) (*.f64 z t))))
6.0ms	(sqrt.f64 (-.f64 (.f64 x y) (.f64 z t)))

simplify112.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

557×	`times-frac_binary64`
537×	`fma-neg_binary64`
342×	`*-commutative_binary64`
337×	`associate-/r*_binary64`
330×	`fma-def_binary64`

Counts

134 → 121

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	138	2631
1	335	2448
2	1184	2366
3	4373	2332
4	4960	2332

prune145.0ms (2.4%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	225	1	226
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	225	3	228

Error

Counts

228 → 3

Alt Table

Status	Error	Program
✓	31.4b	(.f64 (sqrt.f64 (-.f64 (.f64 x y) (.f64 z t))) (sqrt.f64 (-.f64 (.f64 x y) (*.f64 z t))))
✓	0.0b	(fma.f64 x y (neg.f64 (*.f64 z t)))
▶	31.8b	(.f64 (sqrt.f64 (-.f64 (.f64 x y) (.f64 z t))) (.f64 (.f64 (cbrt.f64 (sqrt.f64 (-.f64 (.f64 x y) (.f64 z t)))) (cbrt.f64 (sqrt.f64 (-.f64 (.f64 x y) (.f64 z t))))) (cbrt.f64 (sqrt.f64 (-.f64 (.f64 x y) (*.f64 z t))))))

Compiler

Compiled 6043 to 1064 computations (82.4% saved)

localize20.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (sqrt.f64 (-.f64 (.f64 x y) (.f64 z t))) (.f64 (.f64 (cbrt.f64 (sqrt.f64 (-.f64 (.f64 x y) (.f64 z t)))) (cbrt.f64 (sqrt.f64 (-.f64 (.f64 x y) (.f64 z t))))) (cbrt.f64 (sqrt.f64 (-.f64 (.f64 x y) (*.f64 z t))))))
✓	0.2b	(.f64 (cbrt.f64 (sqrt.f64 (-.f64 (.f64 x y) (.f64 z t)))) (cbrt.f64 (sqrt.f64 (-.f64 (.f64 x y) (*.f64 z t)))))
✓	0.3b	(cbrt.f64 (sqrt.f64 (-.f64 (.f64 x y) (.f64 z t))))
	1.8b	(sqrt.f64 (-.f64 (.f64 x y) (.f64 z t)))

series460.0ms (7.5%)

Counts

3 → 120

Calls

3 calls:

232.0ms

(*.f64 (cbrt.f64 (sqrt.f64 (-.f64 (*.f64 x y) (*.f64 z t)))) (cbrt.f64 (sqrt.f64 (-.f64 (*.f64 x y) (*.f64 z t)))))

174.0ms

(cbrt.f64 (sqrt.f64 (-.f64 (*.f64 x y) (*.f64 z t))))

53.0ms

(*.f64 (sqrt.f64 (-.f64 (*.f64 x y) (*.f64 z t))) (*.f64 (*.f64 (cbrt.f64 (sqrt.f64 (-.f64 (*.f64 x y) (*.f64 z t)))) (cbrt.f64 (sqrt.f64 (-.f64 (*.f64 x y) (*.f64 z t))))) (cbrt.f64 (sqrt.f64 (-.f64 (*.f64 x y) (*.f64 z t))))))

rewrite135.0ms (2.2%)

Algorithm

1×	rewrite-expression-head

Rules

230×	`sqrt-div_binary64`
176×	`cbrt-div_binary64`
140×	`frac-times_binary64`
115×	`flip--_binary64`
115×	`flip3--_binary64`

Counts

3 → 193

Calls

3 calls:

25.0ms

(*.f64 (sqrt.f64 (-.f64 (*.f64 x y) (*.f64 z t))) (*.f64 (*.f64 (cbrt.f64 (sqrt.f64 (-.f64 (*.f64 x y) (*.f64 z t)))) (cbrt.f64 (sqrt.f64 (-.f64 (*.f64 x y) (*.f64 z t))))) (cbrt.f64 (sqrt.f64 (-.f64 (*.f64 x y) (*.f64 z t))))))

12.0ms

(*.f64 (cbrt.f64 (sqrt.f64 (-.f64 (*.f64 x y) (*.f64 z t)))) (cbrt.f64 (sqrt.f64 (-.f64 (*.f64 x y) (*.f64 z t)))))

4.0ms

(cbrt.f64 (sqrt.f64 (-.f64 (*.f64 x y) (*.f64 z t))))

simplify504.0ms (8.2%)

Algorithm

1×	egg-herbie

Rules

587×	`associate-/r*_binary64`
510×	`associate-/l*_binary64`
303×	`*-commutative_binary64`
222×	`fma-def_binary64`
185×	`associate-r_binary64`

Counts

313 → 397

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	649	18330
1	1846	17854
2	5040	17854

prune534.0ms (8.7%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	743	0	743
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	743	3	746

Error

Counts

746 → 3

Alt Table

Status	Error	Program
✓	31.4b	(.f64 (sqrt.f64 (-.f64 (.f64 x y) (.f64 z t))) (sqrt.f64 (-.f64 (.f64 x y) (*.f64 z t))))
✓	0.0b	(fma.f64 x y (neg.f64 (*.f64 z t)))
✓	31.8b	(.f64 (sqrt.f64 (-.f64 (.f64 x y) (.f64 z t))) (.f64 (.f64 (cbrt.f64 (sqrt.f64 (-.f64 (.f64 x y) (.f64 z t)))) (cbrt.f64 (sqrt.f64 (-.f64 (.f64 x y) (.f64 z t))))) (cbrt.f64 (sqrt.f64 (-.f64 (.f64 x y) (*.f64 z t))))))

Compiler

Compiled 47477 to 10858 computations (77.1% saved)

regimes291.0ms (4.7%)

Accuracy

Total 0.0b remaining (19.5%)

Threshold costs 0.0b (19.5%)

Counts

27 → 1

Compiler

Compiled 5025 to 2752 computations (45.2% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	22
1	22	22
2	30	22
3	34	22
4	35	22
5	35	22

end41.0ms (0.7%)

Remove

(sort z t)

(sort x y)

Compiler

Compiled 95 to 50 computations (47.4% saved)

sample1.2s (19.5%)

Algorithm

1×

intervals

Results

417.0ms	8000×	body	128	valid
70.0ms	1321×	body	128	invalid

Compiler

Compiled 109 to 50 computations (54.1% saved)

Iter	Nodes	Cost
0	8	10
1	16	10
2	27	10
3	44	10
4	66	10
5	100	10
6	152	10
7	213	10
8	257	10
9	279	10
10	299	10
11	305	10
12	274	10

Iter	Nodes	Cost
0	8	10
1	16	10
2	27	10
3	44	10
4	66	10
5	100	10
6	152	10
7	213	10
8	257	10
9	279	10
10	299	10
11	305	10
12	274	10

Details

analyze1.9s (31.4%)

sample59.0ms (1%)

simplify27.0ms (0.4%)

prune3.0ms (0%)

localize10.0ms (0.2%)

series21.0ms (0.3%)

rewrite6.0ms (0.1%)

simplify162.0ms (2.6%)

prune35.0ms (0.6%)

localize10.0ms (0.2%)

series19.0ms (0.3%)

rewrite1.0ms (0%)

simplify130.0ms (2.1%)

prune16.0ms (0.3%)

localize13.0ms (0.2%)

series216.0ms (3.5%)

rewrite46.0ms (0.7%)

simplify112.0ms (1.8%)

prune145.0ms (2.4%)

localize20.0ms (0.3%)

series460.0ms (7.5%)

rewrite135.0ms (2.2%)

simplify504.0ms (8.2%)

prune534.0ms (8.7%)

regimes291.0ms (4.7%)

simplify5.0ms (0.1%)

end41.0ms (0.7%)

sample1.2s (19.5%)

Profiling

Iter	Nodes	Cost
0	8	10
1	16	10
2	27	10
3	44	10
4	66	10
5	100	10
6	152	10
7	213	10
8	257	10
9	279	10
10	299	10
11	305	10
12	274	10