Details

analyze7.0ms (0.2%)

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
9.4%	9.4%	81.3%	3
9.4%	9.4%	81.3%	4
16.4%	2.3%	81.3%	5
16.4%	2.3%	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)

sample1.4s (39.5%)

Infinites

0% of outputs are infinite.

Results

1.2s

8256×

body

128

valid

Compiler

Compiled 73 to 43 computations (41.1% saved)

simplify78.0ms (2.1%)

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

prune2.0ms (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

20.3b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	20.3b	(/.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))
✓	20.0b	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (fma.f64 x x (.f64 y y)))

series25.0ms (0.7%)

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))

rewrite14.0ms (0.4%)

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:

11.0ms	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (fma.f64 x x (.f64 y y)))
0.0ms	(fma.f64 x x (*.f64 y y))

simplify54.0ms (1.5%)

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

prune44.0ms (1.2%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	74	2	76
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	75	2	77

Error

0.0b

Counts

77 → 2

Alt Table

Status	Error	Program
	40.7b	(/.f64 (.f64 (-.f64 x y) (+.f64 (pow.f64 x 3) (pow.f64 y 3))) (.f64 (fma.f64 x x (.f64 y y)) (+.f64 (.f64 x x) (-.f64 (.f64 y y) (.f64 x y)))))
▶	0.0b	(*.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (/.f64 (+.f64 x y) (hypot.f64 x y)))

Status

Error

Program

40.7b

(/.f64 (*.f64 (-.f64 x y) (+.f64 (pow.f64 x 3) (pow.f64 y 3))) (*.f64 (fma.f64 x x (*.f64 y y)) (+.f64 (*.f64 x x) (-.f64 (*.f64 y 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 1756 to 474 computations (73% 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)))

series88.0ms (2.4%)

Counts

4 → 96

Calls

4 calls:

53.0ms	(*.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (/.f64 (+.f64 x y) (hypot.f64 x y)))
13.0ms	(hypot.f64 x y)
12.0ms	(/.f64 (-.f64 x y) (hypot.f64 x y))
9.0ms	(/.f64 (+.f64 x y) (hypot.f64 x y))

rewrite35.0ms (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:

12.0ms	(*.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (/.f64 (+.f64 x y) (hypot.f64 x y)))
5.0ms	(/.f64 (-.f64 x y) (hypot.f64 x y))
4.0ms	(/.f64 (+.f64 x y) (hypot.f64 x y))
0.0ms	(hypot.f64 x y)

simplify139.0ms (3.8%)

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

prune191.0ms (5.3%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	300	1	301
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	301	2	303

Error

Counts

303 → 2

Alt Table

Status	Error	Program
	40.7b	(/.f64 (.f64 (-.f64 x y) (+.f64 (pow.f64 x 3) (pow.f64 y 3))) (.f64 (fma.f64 x x (.f64 y y)) (+.f64 (.f64 x x) (-.f64 (.f64 y y) (.f64 x y)))))
▶	0.0b	(*.f64 (/.f64 1 (/.f64 (hypot.f64 x y) (-.f64 x y))) (/.f64 (+.f64 x y) (hypot.f64 x y)))

Status

Error

Program

40.7b

(/.f64 (*.f64 (-.f64 x y) (+.f64 (pow.f64 x 3) (pow.f64 y 3))) (*.f64 (fma.f64 x x (*.f64 y y)) (+.f64 (*.f64 x x) (-.f64 (*.f64 y y) (*.f64 x y)))))

▶

0.0b

(*.f64 (/.f64 1 (/.f64 (hypot.f64 x y) (-.f64 x y))) (/.f64 (+.f64 x y) (hypot.f64 x y)))

Compiler

Compiled 7445 to 1916 computations (74.3% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (hypot.f64 x y) (-.f64 x y))
	0.0b	(/.f64 (+.f64 x y) (hypot.f64 x y))
✓	0.0b	(/.f64 1 (/.f64 (hypot.f64 x y) (-.f64 x y)))
✓	0.0b	(*.f64 (/.f64 1 (/.f64 (hypot.f64 x y) (-.f64 x y))) (/.f64 (+.f64 x y) (hypot.f64 x y)))

series56.0ms (1.5%)

Counts

3 → 72

Calls

3 calls:

27.0ms	(*.f64 (/.f64 1 (/.f64 (hypot.f64 x y) (-.f64 x y))) (/.f64 (+.f64 x y) (hypot.f64 x y)))
15.0ms	(/.f64 1 (/.f64 (hypot.f64 x y) (-.f64 x y)))
14.0ms	(/.f64 (hypot.f64 x y) (-.f64 x y))

rewrite110.0ms (3%)

Algorithm

1×	rewrite-expression-head

Rules

275×	`times-frac_binary64`
211×	`add-sqr-sqrt_binary64`
188×	`*-un-lft-identity_binary64`
128×	`add-cube-cbrt_binary64`
68×	`associate-l_binary64`

Counts

3 → 277

Calls

3 calls:

26.0ms	(*.f64 (/.f64 1 (/.f64 (hypot.f64 x y) (-.f64 x y))) (/.f64 (+.f64 x y) (hypot.f64 x y)))
7.0ms	(/.f64 1 (/.f64 (hypot.f64 x y) (-.f64 x y)))
4.0ms	(/.f64 (hypot.f64 x y) (-.f64 x y))

simplify185.0ms (5.1%)

Algorithm

1×	egg-herbie

Rules

638×	`distribute-rgt-in_binary64`
457×	`fma-def_binary64`
186×	`associate-*l/_binary64`
175×	`associate-r_binary64`
169×	`cancel-sign-sub-inv_binary64`

Counts

349 → 439

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	301	8487
1	810	7567
2	2955	7421
3	5314	7421

prune259.0ms (7.1%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	500	0	500
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	500	2	502

Error

Counts

502 → 2

Alt Table

Status	Error	Program
▶	40.7b	(/.f64 (.f64 (-.f64 x y) (+.f64 (pow.f64 x 3) (pow.f64 y 3))) (.f64 (fma.f64 x x (.f64 y y)) (+.f64 (.f64 x x) (-.f64 (.f64 y y) (.f64 x y)))))
✓	0.0b	(*.f64 (/.f64 1 (/.f64 (hypot.f64 x y) (-.f64 x y))) (/.f64 (+.f64 x y) (hypot.f64 x y)))

Status

Error

Program

▶

40.7b

(/.f64 (*.f64 (-.f64 x y) (+.f64 (pow.f64 x 3) (pow.f64 y 3))) (*.f64 (fma.f64 x x (*.f64 y y)) (+.f64 (*.f64 x x) (-.f64 (*.f64 y y) (*.f64 x y)))))

✓

0.0b

(*.f64 (/.f64 1 (/.f64 (hypot.f64 x y) (-.f64 x y))) (/.f64 (+.f64 x y) (hypot.f64 x y)))

Compiler

Compiled 14013 to 3573 computations (74.5% saved)

localize18.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (.f64 y y) (.f64 x y))
✓	0.1b	(*.f64 (-.f64 x y) (+.f64 (pow.f64 x 3) (pow.f64 y 3)))
✓	0.2b	(.f64 (fma.f64 x x (.f64 y y)) (+.f64 (.f64 x x) (-.f64 (.f64 y y) (*.f64 x y))))
✓	39.9b	(/.f64 (.f64 (-.f64 x y) (+.f64 (pow.f64 x 3) (pow.f64 y 3))) (.f64 (fma.f64 x x (.f64 y y)) (+.f64 (.f64 x x) (-.f64 (.f64 y y) (.f64 x y)))))

series65.0ms (1.8%)

Counts

4 → 96

Calls

4 calls:

33.0ms	(/.f64 (.f64 (-.f64 x y) (+.f64 (pow.f64 x 3) (pow.f64 y 3))) (.f64 (fma.f64 x x (.f64 y y)) (+.f64 (.f64 x x) (-.f64 (.f64 y y) (.f64 x y)))))
12.0ms	(*.f64 (-.f64 x y) (+.f64 (pow.f64 x 3) (pow.f64 y 3)))
12.0ms	(.f64 (fma.f64 x x (.f64 y y)) (+.f64 (.f64 x x) (-.f64 (.f64 y y) (*.f64 x y))))
7.0ms	(-.f64 (.f64 y y) (.f64 x y))

rewrite56.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`*-un-lft-identity_binary64`
20×	`add-cbrt-cube_binary64`
20×	`add-exp-log_binary64`
14×	`add-sqr-sqrt_binary64`
12×	`associate-r_binary64`

Counts

4 → 112

Calls

4 calls:

20.0ms	(/.f64 (.f64 (-.f64 x y) (+.f64 (pow.f64 x 3) (pow.f64 y 3))) (.f64 (fma.f64 x x (.f64 y y)) (+.f64 (.f64 x x) (-.f64 (.f64 y y) (.f64 x y)))))
17.0ms	(*.f64 (-.f64 x y) (+.f64 (pow.f64 x 3) (pow.f64 y 3)))
7.0ms	(.f64 (fma.f64 x x (.f64 y y)) (+.f64 (.f64 x x) (-.f64 (.f64 y y) (*.f64 x y))))
3.0ms	(-.f64 (.f64 y y) (.f64 x y))

simplify116.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

364×	`associate-l_binary64`
341×	`associate-r_binary64`
336×	`fma-neg_binary64`
273×	`times-frac_binary64`
242×	`distribute-rgt-in_binary64`

Counts

208 → 222

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	240	5040
1	791	4326
2	4120	4326
3	5036	4326

prune133.0ms (3.6%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	222	0	222
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	222	2	224

Error

Counts

224 → 2

Alt Table

Status	Error	Program
✓	40.7b	(/.f64 (.f64 (-.f64 x y) (+.f64 (pow.f64 x 3) (pow.f64 y 3))) (.f64 (fma.f64 x x (.f64 y y)) (+.f64 (.f64 x x) (-.f64 (.f64 y y) (.f64 x y)))))
✓	0.0b	(*.f64 (/.f64 1 (/.f64 (hypot.f64 x y) (-.f64 x y))) (/.f64 (+.f64 x y) (hypot.f64 x y)))

Status

Error

Program

✓

40.7b

(/.f64 (*.f64 (-.f64 x y) (+.f64 (pow.f64 x 3) (pow.f64 y 3))) (*.f64 (fma.f64 x x (*.f64 y y)) (+.f64 (*.f64 x x) (-.f64 (*.f64 y y) (*.f64 x y)))))

✓

0.0b

(*.f64 (/.f64 1 (/.f64 (hypot.f64 x y) (-.f64 x y))) (/.f64 (+.f64 x y) (hypot.f64 x y)))

Compiler

Compiled 8756 to 2873 computations (67.2% saved)

regimes452.0ms (12.4%)

Accuracy

Total 0.0b remaining (16.6%)

Threshold costs 0.0b (16.6%)

Counts

145 → 1

Compiler

Compiled 9892 to 5414 computations (45.3% saved)

simplify2.0ms (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

end53.0ms (1.5%)

Compiler: Compiled 89 to 47 computations (47.2% saved)

Details

analyze7.0ms (0.2%)

sample1.4s (39.5%)

simplify78.0ms (2.1%)

prune2.0ms (0.1%)

localize8.0ms (0.2%)

series25.0ms (0.7%)

rewrite14.0ms (0.4%)

simplify54.0ms (1.5%)

prune44.0ms (1.2%)

localize8.0ms (0.2%)

series88.0ms (2.4%)

rewrite35.0ms (1%)

simplify139.0ms (3.8%)

prune191.0ms (5.3%)

localize8.0ms (0.2%)

series56.0ms (1.5%)

rewrite110.0ms (3%)

simplify185.0ms (5.1%)

prune259.0ms (7.1%)

localize18.0ms (0.5%)

series65.0ms (1.8%)

rewrite56.0ms (1.5%)

simplify116.0ms (3.2%)

prune133.0ms (3.6%)

regimes452.0ms (12.4%)

simplify2.0ms (0.1%)

end53.0ms (1.5%)

Profiling