Details

analyze15.0ms (0.4%)

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)

sample1.3s (39.2%)

Results

1.0s

8256×

body

128

valid

Compiler

Compiled 73 to 43 computations (41.1% saved)

simplify80.0ms (2.4%)

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

22.5b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	22.5b	(/.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 (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (-.f64 x y) (+.f64 x y))
✓	0.0b	(fma.f64 x x (*.f64 y y))
✓	22.2b	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (fma.f64 x x (.f64 y y)))

series34.0ms (1%)

Counts

3 → 72

Calls

3 calls:

21.0ms	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (fma.f64 x x (.f64 y y)))
7.0ms	(*.f64 (-.f64 x y) (+.f64 x y))
6.0ms	(fma.f64 x x (*.f64 y y))

rewrite25.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`*-un-lft-identity_binary64`
11×	`add-sqr-sqrt_binary64`
10×	`add-cbrt-cube_binary64`
10×	`add-exp-log_binary64`
8×	`associate-/l/_binary64`

Counts

3 → 74

Calls

3 calls:

12.0ms	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (fma.f64 x x (.f64 y y)))
7.0ms	(*.f64 (-.f64 x y) (+.f64 x y))
0.0ms	(fma.f64 x x (*.f64 y y))

simplify68.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

724×	`times-frac_binary64`
709×	`fma-def_binary64`
675×	`associate-/l*_binary64`
185×	`associate-/l/_binary64`
177×	`distribute-rgt-in_binary64`

Counts

146 → 135

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	149	2451
1	448	2215
2	1939	2177
3	5171	2177

prune75.0ms (2.3%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	131	4	135
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	132	4	136

Error

Counts

136 → 4

Alt Table

Status	Error	Program
	22.3b	(/.f64 (.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (+.f64 x y)) (sqrt.f64 (fma.f64 x x (.f64 y y))))
	22.4b	(/.f64 (-.f64 x y) (/.f64 (fma.f64 x x (*.f64 y y)) (+.f64 x y)))
	22.5b	(/.f64 1 (/.f64 (fma.f64 x x (.f64 y y)) (.f64 (-.f64 x y) (+.f64 x y))))
▶	0.0b	(*.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (/.f64 (+.f64 x y) (hypot.f64 x y)))

Compiler

Compiled 3146 to 730 computations (76.8% saved)

localize7.0ms (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)))

series57.0ms (1.7%)

Counts

4 → 96

Calls

4 calls:

26.0ms	(*.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (/.f64 (+.f64 x y) (hypot.f64 x y)))
11.0ms	(hypot.f64 x y)
10.0ms	(/.f64 (+.f64 x y) (hypot.f64 x y))
9.0ms	(/.f64 (-.f64 x y) (hypot.f64 x y))

rewrite34.0ms (1%)

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:

13.0ms	(*.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)

simplify144.0ms (4.4%)

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

prune469.0ms (14.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	300	1	301
Fresh	2	1	3
Picked	0	1	1
Done	0	0	0
Total	302	3	305

Error

Counts

305 → 3

Alt Table

Status	Error	Program
	22.4b	(/.f64 (-.f64 x y) (/.f64 (fma.f64 x x (*.f64 y y)) (+.f64 x y)))
▶	0.0b	(log1p.f64 (expm1.f64 (*.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (/.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)))

Compiler

Compiled 7430 to 1906 computations (74.3% saved)

localize11.0ms (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	(/.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)))
✓	0.4b	(expm1.f64 (*.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (/.f64 (+.f64 x y) (hypot.f64 x y))))

series43.0ms (1.3%)

Counts

1 → 24

Calls

1 calls:

42.0ms

(expm1.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×	`log1p-expm1-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

(expm1.f64 (*.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (/.f64 (+.f64 x y) (hypot.f64 x y))))

simplify67.0ms (2%)

Algorithm

1×	egg-herbie

Rules

709×	`fma-neg_binary64`
644×	`cancel-sign-sub-inv_binary64`
584×	`associate-/l/_binary64`
292×	`times-frac_binary64`
209×	`distribute-rgt-neg-in_binary64`

Counts

35 → 28

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	72	1145
1	186	1036
2	579	1018
3	2512	1000
4	4963	982
5	5180	982

prune172.0ms (5.2%)

Pruning

3 alts after pruning (1 fresh and 2 done)

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

Error

Counts

248 → 3

Alt Table

Status	Error	Program
▶	22.4b	(/.f64 (-.f64 x y) (/.f64 (fma.f64 x x (*.f64 y y)) (+.f64 x y)))
✓	0.0b	(log1p.f64 (expm1.f64 (*.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (/.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)))

Compiler

Compiled 6421 to 1840 computations (71.3% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(fma.f64 x x (*.f64 y y))
✓	0.0b	(/.f64 (-.f64 x y) (/.f64 (fma.f64 x x (*.f64 y y)) (+.f64 x y)))
✓	21.3b	(/.f64 (fma.f64 x x (*.f64 y y)) (+.f64 x y))

series27.0ms (0.8%)

Counts

2 → 48

Calls

2 calls:

18.0ms	(/.f64 (-.f64 x y) (/.f64 (fma.f64 x x (*.f64 y y)) (+.f64 x y)))
9.0ms	(/.f64 (fma.f64 x x (*.f64 y y)) (+.f64 x y))

rewrite48.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

174×	`times-frac_binary64`
160×	`*-un-lft-identity_binary64`
116×	`add-sqr-sqrt_binary64`
78×	`add-cube-cbrt_binary64`
22×	`associate-/r*_binary64`

Counts

2 → 168

Calls

2 calls:

21.0ms	(/.f64 (-.f64 x y) (/.f64 (fma.f64 x x (*.f64 y y)) (+.f64 x y)))
4.0ms	(/.f64 (fma.f64 x x (*.f64 y y)) (+.f64 x y))

simplify168.0ms (5.1%)

Algorithm

1×	egg-herbie

Rules

650×	`times-frac_binary64`
453×	`distribute-rgt-in_binary64`
377×	`fma-neg_binary64`
349×	`fma-def_binary64`
256×	`associate-/r/_binary64`

Counts

216 → 267

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	273	6857
1	767	6286
2	2461	6244
3	4944	6232
4	5182	6232

prune127.0ms (3.9%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	285	0	285
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	285	3	288

Error

Counts

288 → 3

Alt Table

Status	Error	Program
✓	22.4b	(/.f64 (-.f64 x y) (/.f64 (fma.f64 x x (*.f64 y y)) (+.f64 x y)))
✓	0.0b	(log1p.f64 (expm1.f64 (*.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (/.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)))

Compiler

Compiled 7657 to 1208 computations (84.2% saved)

regimes243.0ms (7.4%)

Accuracy

Total 0.0b remaining (35.8%)

Threshold costs 0.0b (35.8%)

Counts

88 → 1

Compiler

Compiled 4200 to 2443 computations (41.8% 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	9	22
1	13	22
2	18	22
3	20	22
4	21	22
5	21	22

end61.0ms (1.9%)

Compiler: Compiled 86 to 42 computations (51.2% saved)

Details

analyze15.0ms (0.4%)

sample1.3s (39.2%)

simplify80.0ms (2.4%)

prune3.0ms (0.1%)

localize9.0ms (0.3%)

series34.0ms (1%)

rewrite25.0ms (0.7%)

simplify68.0ms (2.1%)

prune75.0ms (2.3%)

localize7.0ms (0.2%)

series57.0ms (1.7%)

rewrite34.0ms (1%)

simplify144.0ms (4.4%)

prune469.0ms (14.3%)

localize11.0ms (0.3%)

series43.0ms (1.3%)

rewrite1.0ms (0%)

simplify67.0ms (2%)

prune172.0ms (5.2%)

localize8.0ms (0.2%)

series27.0ms (0.8%)

rewrite48.0ms (1.5%)

simplify168.0ms (5.1%)

prune127.0ms (3.9%)

regimes243.0ms (7.4%)

simplify3.0ms (0.1%)

end61.0ms (1.9%)

Profiling