Details

analyze257.0ms (6%)

Algorithm

1×

Search

True	Other	False	Iter
0%	18.7%	81.3%	0
0%	18.7%	81.3%	1
0%	18.7%	81.3%	2
0%	18.7%	81.3%	3
0%	18.7%	81.3%	4
4.7%	14%	81.3%	5
5.3%	13.5%	81.3%	6
18.1%	0.6%	81.3%	7
18.1%	0.6%	81.3%	8
18.6%	0.1%	81.3%	9
18.6%	0.1%	81.3%	10
18.7%	0%	81.3%	11
18.7%	0%	81.3%	12
18.7%	0%	81.3%	13
18.7%	0%	81.3%	14

Compiler

Compiled 28 to 17 computations (39.3% saved)

sample30.0ms (0.7%)

Algorithm

1×

intervals

Results

15.0ms	256×	body	128	valid
6.0ms	256×	pre	128	true

Compiler

Compiled 47 to 28 computations (40.4% saved)

simplify78.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

917×	`times-frac_binary64`
816×	`unsub-neg_binary64`
772×	`fma-def_binary64`
484×	`fma-neg_binary64`
376×	`sub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	20
1	24	20
2	55	20
3	112	20
4	271	20
5	657	20
6	1234	20
7	2620	20
8	3288	20
9	4652	20
10	5075	20

prune3.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

20.6b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	20.6b	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (fma.f64 x x (.f64 y y)))

Compiler

Compiled 63 to 27 computations (57.1% saved)

localize8.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x x (*.f64 y y))
✓	20.3b	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (fma.f64 x x (.f64 y y)))

series25.0ms (0.6%)

Counts

2 → 48

Calls

2 calls:

19.0ms	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (fma.f64 x x (.f64 y y)))
6.0ms	(fma.f64 x x (*.f64 y y))

rewrite10.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`associate-/l/_binary64`
7×	`add-cbrt-cube_binary64`
7×	`add-exp-log_binary64`
4×	`frac-times_binary64`
4×	`*-un-lft-identity_binary64`

Counts

2 → 41

Calls

2 calls:

7.0ms	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (fma.f64 x x (.f64 y y)))
0.0ms	(fma.f64 x x (*.f64 y y))

simplify53.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

843×	`distribute-rgt-in_binary64`
815×	`distribute-lft-in_binary64`
413×	`times-frac_binary64`
413×	`fma-def_binary64`
73×	`cancel-sign-sub-inv_binary64`

Counts

89 → 76

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	108	1667
1	332	1473
2	1320	1435
3	5254	1435

prune39.0ms (0.9%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	73	3	76
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	74	3	77

Error

0.0b

Counts

77 → 3

Alt Table

Status	Error	Program
	26.2b	(fma.f64 2 (/.f64 (.f64 x x) (.f64 y y)) -1)
	21.5b	(/.f64 (/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (.f64 (cbrt.f64 (fma.f64 x x (.f64 y y))) (cbrt.f64 (fma.f64 x x (.f64 y y))))) (cbrt.f64 (fma.f64 x x (*.f64 y y))))
▶	0.0b	(*.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (/.f64 (+.f64 x y) (hypot.f64 x y)))

Compiler

Compiled 1782 to 478 computations (73.2% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(hypot.f64 x y)
✓	0.0b	(/.f64 (+.f64 x y) (hypot.f64 x y))
✓	0.0b	(/.f64 (-.f64 x y) (hypot.f64 x y))
✓	0.0b	(*.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (/.f64 (+.f64 x y) (hypot.f64 x y)))

series67.0ms (1.6%)

Counts

4 → 96

Calls

4 calls:

29.0ms	(*.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (/.f64 (+.f64 x y) (hypot.f64 x y)))
14.0ms	(/.f64 (-.f64 x y) (hypot.f64 x y))
12.0ms	(hypot.f64 x y)
11.0ms	(/.f64 (+.f64 x y) (hypot.f64 x y))

rewrite35.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

68×	`*-un-lft-identity_binary64`
66×	`add-sqr-sqrt_binary64`
58×	`times-frac_binary64`
40×	`add-cube-cbrt_binary64`
20×	`add-cbrt-cube_binary64`

Counts

4 → 146

Calls

4 calls:

14.0ms	(*.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (/.f64 (+.f64 x y) (hypot.f64 x y)))
4.0ms	(/.f64 (-.f64 x y) (hypot.f64 x y))
4.0ms	(/.f64 (+.f64 x y) (hypot.f64 x y))
0.0ms	(hypot.f64 x y)

simplify140.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

776×	`times-frac_binary64`
614×	`fma-neg_binary64`
593×	`fma-def_binary64`
222×	`sub-neg_binary64`
164×	`associate-*l/_binary64`

Counts

242 → 259

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	277	5087
1	854	4676
2	2705	4565
3	4842	4565
4	5181	4565

prune209.0ms (4.8%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	298	3	301
Fresh	2	0	2
Picked	1	0	1
Done	0	0	0
Total	301	3	304

Error

Counts

304 → 3

Alt Table

Status	Error	Program
▶	0.0b	(.f64 (.f64 (cbrt.f64 (.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (/.f64 (+.f64 x y) (hypot.f64 x y)))) (cbrt.f64 (.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (/.f64 (+.f64 x y) (hypot.f64 x y))))) (cbrt.f64 (*.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (/.f64 (+.f64 x y) (hypot.f64 x y)))))
	0.2b	(*.f64 (-.f64 x y) (/.f64 (/.f64 (+.f64 x y) (hypot.f64 x y)) (hypot.f64 x y)))
	0.5b	(*.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (/.f64 (/.f64 (+.f64 x y) (sqrt.f64 (hypot.f64 x y))) (sqrt.f64 (hypot.f64 x y))))

Compiler

Compiled 7527 to 1920 computations (74.5% saved)

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(/.f64 (+.f64 x y) (hypot.f64 x y))
✓	0.0b	(cbrt.f64 (*.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (/.f64 (+.f64 x y) (hypot.f64 x y))))
	0.0b	(/.f64 (-.f64 x y) (hypot.f64 x y))
	0.0b	(*.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (/.f64 (+.f64 x y) (hypot.f64 x y)))

series56.0ms (1.3%)

Counts

1 → 24

Calls

1 calls:

56.0ms

(cbrt.f64 (*.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (/.f64 (+.f64 x y) (hypot.f64 x y))))

rewrite7.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`cbrt-div_binary64`
1×	`*-un-lft-identity_binary64`
1×	`add-sqr-sqrt_binary64`
1×	`cbrt-prod_binary64`
1×	`associate-*r/_binary64`

Counts

1 → 14

Calls

1 calls:

7.0ms

(cbrt.f64 (*.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (/.f64 (+.f64 x y) (hypot.f64 x y))))

simplify62.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

779×	`fma-neg_binary64`
396×	`times-frac_binary64`
391×	`associate-r_binary64`
332×	`associate-l_binary64`
265×	`associate-/l*_binary64`

Counts

38 → 38

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	90	1104
1	238	1044
2	784	1008
3	4106	1002
4	4959	1002

prune573.0ms (13.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	765	0	765
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	765	3	768

Error

Counts

768 → 3

Alt Table

Status	Error	Program
✓	0.0b	(.f64 (.f64 (cbrt.f64 (.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (/.f64 (+.f64 x y) (hypot.f64 x y)))) (cbrt.f64 (.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (/.f64 (+.f64 x y) (hypot.f64 x y))))) (cbrt.f64 (*.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (/.f64 (+.f64 x y) (hypot.f64 x y)))))
▶	0.2b	(*.f64 (-.f64 x y) (/.f64 (/.f64 (+.f64 x y) (hypot.f64 x y)) (hypot.f64 x y)))
	0.5b	(*.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (/.f64 (/.f64 (+.f64 x y) (sqrt.f64 (hypot.f64 x y))) (sqrt.f64 (hypot.f64 x y))))

Compiler

Compiled 45146 to 5542 computations (87.7% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(hypot.f64 x y)
	0.0b	(/.f64 (+.f64 x y) (hypot.f64 x y))
✓	0.0b	(/.f64 (/.f64 (+.f64 x y) (hypot.f64 x y)) (hypot.f64 x y))
✓	0.2b	(*.f64 (-.f64 x y) (/.f64 (/.f64 (+.f64 x y) (hypot.f64 x y)) (hypot.f64 x y)))

series39.0ms (0.9%)

Counts

2 → 48

Calls

2 calls:

26.0ms	(*.f64 (-.f64 x y) (/.f64 (/.f64 (+.f64 x y) (hypot.f64 x y)) (hypot.f64 x y)))
13.0ms	(/.f64 (/.f64 (+.f64 x y) (hypot.f64 x y)) (hypot.f64 x y))

rewrite46.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

183×	`times-frac_binary64`
137×	`*-un-lft-identity_binary64`
104×	`add-sqr-sqrt_binary64`
93×	`add-cube-cbrt_binary64`
52×	`associate-r_binary64`

Counts

2 → 166

Calls

2 calls:

17.0ms	(*.f64 (-.f64 x y) (/.f64 (/.f64 (+.f64 x y) (hypot.f64 x y)) (hypot.f64 x y)))
6.0ms	(/.f64 (/.f64 (+.f64 x y) (hypot.f64 x y)) (hypot.f64 x y))

simplify163.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

438×	`distribute-rgt-in_binary64`
423×	`distribute-lft-in_binary64`
253×	`fma-def_binary64`
184×	`div-sub_binary64`
164×	`associate-/l/_binary64`

Counts

214 → 240

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	273	6076
1	679	5610
2	2284	5306
3	4716	5225
4	5210	5225

prune281.0ms (6.5%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	385	0	385
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	385	3	388

Error

Counts

388 → 3

Alt Table

Status	Error	Program
✓	0.0b	(.f64 (.f64 (cbrt.f64 (.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (/.f64 (+.f64 x y) (hypot.f64 x y)))) (cbrt.f64 (.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (/.f64 (+.f64 x y) (hypot.f64 x y))))) (cbrt.f64 (*.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (/.f64 (+.f64 x y) (hypot.f64 x y)))))
✓	0.2b	(*.f64 (-.f64 x y) (/.f64 (/.f64 (+.f64 x y) (hypot.f64 x y)) (hypot.f64 x y)))
	0.5b	(*.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (/.f64 (/.f64 (+.f64 x y) (sqrt.f64 (hypot.f64 x y))) (sqrt.f64 (hypot.f64 x y))))

Compiler

Compiled 10129 to 2382 computations (76.5% saved)

regimes1.2s (27.3%)

Accuracy

Total 0.0b remaining (44.9%)

Threshold costs 0.0b (44.9%)

Counts

367 → 1

Compiler

Compiled 33517 to 14048 computations (58.1% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	25
1	17	25
2	21	25
3	23	25
4	24	25
5	23	25

end0.0ms (0%)

Compiler: Compiled 19 to 10 computations (47.4% saved)

sample920.0ms (21.4%)

Algorithm

1×

intervals

Results

397.0ms	8000×	body	128	valid
179.0ms	8000×	pre	128	true

Compiler

Compiled 141 to 58 computations (58.9% saved)

Details

analyze257.0ms (6%)

sample30.0ms (0.7%)

simplify78.0ms (1.8%)

prune3.0ms (0.1%)

localize8.0ms (0.2%)

series25.0ms (0.6%)

rewrite10.0ms (0.2%)

simplify53.0ms (1.2%)

prune39.0ms (0.9%)

localize8.0ms (0.2%)

series67.0ms (1.6%)

rewrite35.0ms (0.8%)

simplify140.0ms (3.2%)

prune209.0ms (4.8%)

localize12.0ms (0.3%)

series56.0ms (1.3%)

rewrite7.0ms (0.2%)

simplify62.0ms (1.4%)

prune573.0ms (13.3%)

localize8.0ms (0.2%)

series39.0ms (0.9%)

rewrite46.0ms (1.1%)

simplify163.0ms (3.8%)

prune281.0ms (6.5%)

regimes1.2s (27.3%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample920.0ms (21.4%)

Profiling