Details

analyze2.0s (37.2%)

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
0%	18.7%	81.3%	5
0%	18.7%	81.3%	6
0%	18.7%	81.3%	7
0%	18.7%	81.3%	8
0%	18.7%	81.3%	9
0%	18.7%	81.3%	10
0%	18.7%	81.3%	11
0%	18.7%	81.3%	12
0%	18.7%	81.3%	13
0%	18.7%	81.3%	14

Compiler

Compiled 28 to 17 computations (39.3% saved)

sample1.3s (24.2%)

Results

1.0s

8256×

body

128

valid

Compiler

Compiled 73 to 43 computations (41.1% saved)

simplify79.0ms (1.5%)

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

23.5b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	23.5b	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (fma.f64 x x (.f64 y y)))

Compiler

Compiled 63 to 27 computations (57.1% saved)

localize9.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x x (*.f64 y y))
✓	23.2b	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (fma.f64 x x (.f64 y y)))

series25.0ms (0.5%)

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))

simplify51.0ms (0.9%)

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

prune41.0ms (0.8%)

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
▶	0.0b	(*.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (/.f64 (+.f64 x y) (hypot.f64 x y)))
	23.5b	(/.f64 (/.f64 (.f64 (-.f64 x y) (+.f64 x y)) 1) (fma.f64 x x (.f64 y y)))
	23.5b	(/.f64 1 (/.f64 (fma.f64 x x (.f64 y y)) (.f64 (-.f64 x y) (+.f64 x y))))

Compiler

Compiled 1764 to 480 computations (72.8% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	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)))

series66.0ms (1.2%)

Counts

3 → 72

Calls

3 calls:

29.0ms	(/.f64 (+.f64 x y) (hypot.f64 x y))
27.0ms	(*.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (/.f64 (+.f64 x y) (hypot.f64 x y)))
10.0ms	(/.f64 (-.f64 x y) (hypot.f64 x y))

rewrite34.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

67×	`*-un-lft-identity_binary64`
65×	`add-sqr-sqrt_binary64`
58×	`times-frac_binary64`
39×	`add-cube-cbrt_binary64`
19×	`associate-l_binary64`

Counts

3 → 136

Calls

3 calls:

13.0ms	(*.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (/.f64 (+.f64 x y) (hypot.f64 x y)))
6.0ms	(/.f64 (-.f64 x y) (hypot.f64 x y))
4.0ms	(/.f64 (+.f64 x y) (hypot.f64 x y))

simplify167.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

614×	`times-frac_binary64`
493×	`distribute-rgt-in_binary64`
464×	`fma-def_binary64`
222×	`cancel-sign-sub-inv_binary64`
176×	`sub-neg_binary64`

Counts

208 → 216

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	240	4519
1	735	4135
2	2321	4033
3	5136	4033

prune373.0ms (7%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	214	2	216
Fresh	1	1	2
Picked	1	0	1
Done	0	0	0
Total	216	3	219

Error

Counts

219 → 3

Alt Table

Status	Error	Program
	10.1b	(.f64 (sqrt.f64 (/.f64 (-.f64 x y) (hypot.f64 x y))) (.f64 (sqrt.f64 (/.f64 (-.f64 x y) (hypot.f64 x y))) (/.f64 (+.f64 x y) (hypot.f64 x y))))
▶	0.0b	(expm1.f64 (log1p.f64 (*.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (/.f64 (+.f64 x y) (hypot.f64 x y)))))
	23.5b	(/.f64 1 (/.f64 (fma.f64 x x (.f64 y y)) (.f64 (-.f64 x y) (+.f64 x y))))

Compiler

Compiled 5367 to 1139 computations (78.8% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	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)))
✓	2.2b	(log1p.f64 (*.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (/.f64 (+.f64 x y) (hypot.f64 x y))))

series54.0ms (1%)

Counts

1 → 24

Calls

1 calls:

54.0ms

(log1p.f64 (*.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (/.f64 (+.f64 x y) (hypot.f64 x y))))

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

2×	`expm1-log1p-u_binary64`
1×	`*-un-lft-identity_binary64`
1×	`add-sqr-sqrt_binary64`
1×	`add-cube-cbrt_binary64`
1×	`add-cbrt-cube_binary64`

Counts

1 → 11

Calls

1 calls:

0.0ms

(log1p.f64 (*.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (/.f64 (+.f64 x y) (hypot.f64 x y))))

simplify49.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

833×	`associate-/l*_binary64`
483×	`cancel-sign-sub-inv_binary64`
284×	`fma-neg_binary64`
282×	`associate-/r/_binary64`
226×	`sub-neg_binary64`

Counts

35 → 40

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	80	1039
1	197	960
2	553	960
3	2060	960
4	5038	960

prune198.0ms (3.7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	256	0	256
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	256	3	259

Error

Counts

259 → 3

Alt Table

Status	Error	Program
▶	10.1b	(.f64 (sqrt.f64 (/.f64 (-.f64 x y) (hypot.f64 x y))) (.f64 (sqrt.f64 (/.f64 (-.f64 x y) (hypot.f64 x y))) (/.f64 (+.f64 x y) (hypot.f64 x y))))
✓	0.0b	(expm1.f64 (log1p.f64 (*.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (/.f64 (+.f64 x y) (hypot.f64 x y)))))
	23.5b	(/.f64 1 (/.f64 (fma.f64 x x (.f64 y y)) (.f64 (-.f64 x y) (+.f64 x y))))

Compiler

Compiled 6756 to 2047 computations (69.7% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series73.0ms (1.4%)

Counts

2 → 48

Calls

2 calls:

39.0ms

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

34.0ms

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

rewrite53.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

59×	`add-sqr-sqrt_binary64`
48×	`*-un-lft-identity_binary64`
47×	`times-frac_binary64`
44×	`associate-l_binary64`
42×	`sqrt-prod_binary64`

Counts

2 → 110

Calls

2 calls:

18.0ms

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

18.0ms

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

simplify119.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

875×	`fma-def_binary64`
285×	`associate-r_binary64`
241×	`times-frac_binary64`
238×	`*-commutative_binary64`
235×	`associate-l_binary64`

Counts

158 → 225

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	353	5190
1	1055	4771
2	4177	4712
3	5001	4712

prune340.0ms (6.4%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	417	0	417
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	417	3	420

Error

Counts

420 → 3

Alt Table

Status	Error	Program
✓	10.1b	(.f64 (sqrt.f64 (/.f64 (-.f64 x y) (hypot.f64 x y))) (.f64 (sqrt.f64 (/.f64 (-.f64 x y) (hypot.f64 x y))) (/.f64 (+.f64 x y) (hypot.f64 x y))))
✓	0.0b	(expm1.f64 (log1p.f64 (*.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (/.f64 (+.f64 x y) (hypot.f64 x y)))))
	23.5b	(/.f64 1 (/.f64 (fma.f64 x x (.f64 y y)) (.f64 (-.f64 x y) (+.f64 x y))))

Compiler

Compiled 14608 to 3089 computations (78.9% saved)

regimes222.0ms (4.2%)

Accuracy

Total 0.0b remaining (43%)

Threshold costs 0.0b (43%)

Counts

82 → 1

Compiler

Compiled 4204 to 2474 computations (41.2% saved)

simplify4.0ms (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	26
1	15	26
2	20	26
3	22	26
4	23	26
5	23	26

end63.0ms (1.2%)

Compiler: Compiled 102 to 50 computations (51% saved)

Details

analyze2.0s (37.2%)

sample1.3s (24.2%)

simplify79.0ms (1.5%)

prune3.0ms (0.1%)

localize9.0ms (0.2%)

series25.0ms (0.5%)

rewrite10.0ms (0.2%)

simplify51.0ms (0.9%)

prune41.0ms (0.8%)

localize8.0ms (0.1%)

series66.0ms (1.2%)

rewrite34.0ms (0.6%)

simplify167.0ms (3.1%)

prune373.0ms (7%)

localize10.0ms (0.2%)

series54.0ms (1%)

rewrite1.0ms (0%)

simplify49.0ms (0.9%)

prune198.0ms (3.7%)

localize11.0ms (0.2%)

series73.0ms (1.4%)

rewrite53.0ms (1%)

simplify119.0ms (2.2%)

prune340.0ms (6.4%)

regimes222.0ms (4.2%)

simplify4.0ms (0.1%)

end63.0ms (1.2%)

Profiling