Details

analyze76.0ms (2.9%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
25%	74.9%	0.1%	5
25%	50%	25.1%	6
25%	31.2%	43.8%	7
31.2%	25%	43.8%	8
39%	17.2%	43.8%	9
42.9%	13.3%	43.8%	10
47.2%	9%	43.8%	11
49.4%	6.8%	43.8%	12
51.6%	4.6%	43.8%	13
52.7%	3.5%	43.8%	14

Compiler

Compiled 18 to 8 computations (55.6% saved)

sample28.0ms (1.1%)

Algorithm

1×

intervals

Results

8.0ms

256×

body

128

valid

Compiler

Compiled 37 to 17 computations (54.1% saved)

simplify9.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

28×	`fma-def_binary64`
4×	`*-commutative_binary64`
4×	`associate-+l+_binary64`
4×	`associate-r_binary64`
3×	`+-commutative_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	8	20
1	15	15
2	30	11
3	49	11
4	63	11
5	67	11
6	65	11

prune3.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

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

Error

0.0b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.1b	(fma.f64 y (.f64 y 3) (.f64 x x))
	0.1b	(+.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 y y)) (.f64 y y))

Compiler

Compiled 79 to 36 computations (54.4% saved)

localize5.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 y (.f64 y 3) (.f64 x x))

series7.0ms (0.3%)

Counts

1 → 24

Calls

1 calls:

7.0ms

(fma.f64 y (*.f64 y 3) (*.f64 x x))

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:

0.0ms

(fma.f64 y (*.f64 y 3) (*.f64 x x))

simplify55.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

911×	`fma-def_binary64`
466×	`distribute-rgt-in_binary64`
460×	`distribute-lft-in_binary64`
356×	`unswap-sqr_binary64`
323×	`*-commutative_binary64`

Counts

34 → 24

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	22	394
1	35	371
2	66	371
3	184	371
4	793	371
5	3022	371
6	4320	371
7	5097	371

prune18.0ms (0.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	22	2	24
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	22	4	26

Error

0.0b

Counts

26 → 4

Alt Table

Status	Error	Program
▶	0.1b	(+.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 y y)) (.f64 y y))
	0.3b	(.f64 (sqrt.f64 (fma.f64 y (.f64 y 3) (.f64 x x))) (sqrt.f64 (fma.f64 y (.f64 y 3) (*.f64 x x))))
	1.2b	(.f64 (.f64 (cbrt.f64 (fma.f64 y (.f64 y 3) (.f64 x x))) (cbrt.f64 (fma.f64 y (.f64 y 3) (.f64 x x)))) (cbrt.f64 (fma.f64 y (.f64 y 3) (.f64 x x))))
✓	0.1b	(fma.f64 y (.f64 y 3) (.f64 x x))

Compiler

Compiled 435 to 221 computations (49.2% saved)

localize8.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 x x) (.f64 y y))
✓	0.0b	(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 y y))
✓	0.1b	(+.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 y y)) (.f64 y y))

series22.0ms (0.9%)

Counts

3 → 72

Calls

3 calls:

8.0ms	(+.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 y y)) (.f64 y y))
8.0ms	(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 y y))
6.0ms	(+.f64 (.f64 x x) (.f64 y y))

rewrite19.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`add-log-exp_binary64`
10×	`sum-log_binary64`
7×	`fma-def_binary64`
5×	`*-un-lft-identity_binary64`
5×	`add-sqr-sqrt_binary64`

Counts

3 → 51

Calls

3 calls:

8.0ms	(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 y y))
6.0ms	(+.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 y y)) (.f64 y y))
3.0ms	(+.f64 (.f64 x x) (.f64 y y))

simplify81.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

728×	`fma-neg_binary64`
620×	`fma-def_binary64`
389×	`distribute-rgt-in_binary64`
337×	`distribute-lft-in_binary64`
286×	`unswap-sqr_binary64`

Counts

123 → 94

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	77	1464
1	249	1343
2	745	1260
3	3112	1256
4	4528	1256
5	5022	1256

prune68.0ms (2.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	90	4	94
Fresh	1	1	2
Picked	1	0	1
Done	0	1	1
Total	92	6	98

Error

0.0b

Counts

98 → 6

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 y (.f64 y 3) (.f64 x x))
	48.8b	(+.f64 (/.f64 (+.f64 (pow.f64 (+.f64 (.f64 x x) (.f64 y y)) 3) (pow.f64 (.f64 y y) 3)) (+.f64 (.f64 (+.f64 (.f64 x x) (.f64 y y)) (+.f64 (.f64 x x) (.f64 y y))) (-.f64 (.f64 (.f64 y y) (.f64 y y)) (.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 y y))))) (.f64 y y))
	0.8b	(+.f64 (fma.f64 (.f64 (cbrt.f64 (+.f64 (.f64 x x) (.f64 y y))) (cbrt.f64 (+.f64 (.f64 x x) (.f64 y y)))) (cbrt.f64 (+.f64 (.f64 x x) (.f64 y y))) (.f64 y y)) (*.f64 y y))
▶	0.2b	(fma.f64 (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 y y))) (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 y y))) (*.f64 y y))
	1.0b	(+.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 2 (.f64 y y) (.f64 x x))) (cbrt.f64 (fma.f64 2 (.f64 y y) (.f64 x x)))) (cbrt.f64 (fma.f64 2 (.f64 y y) (.f64 x x)))) (*.f64 y y))
	0.3b	(.f64 (sqrt.f64 (fma.f64 y (.f64 y 3) (.f64 x x))) (sqrt.f64 (fma.f64 y (.f64 y 3) (*.f64 x x))))

Compiler

Compiled 2312 to 539 computations (76.7% saved)

localize7.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(+.f64 (.f64 x x) (.f64 y y))
	0.0b	(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 y y))
✓	0.2b	(fma.f64 (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 y y))) (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 y y))) (*.f64 y y))
✓	6.0b	(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 y y)))

series111.0ms (4.3%)

Counts

2 → 48

Calls

2 calls:

94.0ms

(fma.f64 (sqrt.f64 (+.f64 (+.f64 (*.f64 x x) (*.f64 y y)) (*.f64 y y))) (sqrt.f64 (+.f64 (+.f64 (*.f64 x x) (*.f64 y y)) (*.f64 y y))) (*.f64 y y))

17.0ms

(sqrt.f64 (+.f64 (+.f64 (*.f64 x x) (*.f64 y y)) (*.f64 y y)))

rewrite6.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

5×	`add-sqr-sqrt_binary64`
3×	`*-un-lft-identity_binary64`
3×	`sqrt-prod_binary64`
3×	`add-cube-cbrt_binary64`
3×	`pow1_binary64`

Counts

2 → 28

Calls

2 calls:

4.0ms

(sqrt.f64 (+.f64 (+.f64 (*.f64 x x) (*.f64 y y)) (*.f64 y y)))

0.0ms

(fma.f64 (sqrt.f64 (+.f64 (+.f64 (*.f64 x x) (*.f64 y y)) (*.f64 y y))) (sqrt.f64 (+.f64 (+.f64 (*.f64 x x) (*.f64 y y)) (*.f64 y y))) (*.f64 y y))

simplify44.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

707×	`times-frac_binary64`
352×	`fma-def_binary64`
323×	`associate-r_binary64`
321×	`associate-/l*_binary64`
279×	`associate-l_binary64`

Counts

76 → 84

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	110	1723
1	304	1313
2	956	1216
3	4994	1216

prune209.0ms (8%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	259	1	260
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	259	7	266

Error

0.0b

Counts

266 → 7

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 y (.f64 y 3) (.f64 x x))
	48.8b	(+.f64 (/.f64 (+.f64 (pow.f64 (+.f64 (.f64 x x) (.f64 y y)) 3) (pow.f64 (.f64 y y) 3)) (+.f64 (.f64 (+.f64 (.f64 x x) (.f64 y y)) (+.f64 (.f64 x x) (.f64 y y))) (-.f64 (.f64 (.f64 y y) (.f64 y y)) (.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 y y))))) (.f64 y y))
	0.8b	(+.f64 (fma.f64 (.f64 (cbrt.f64 (+.f64 (.f64 x x) (.f64 y y))) (cbrt.f64 (+.f64 (.f64 x x) (.f64 y y)))) (cbrt.f64 (+.f64 (.f64 x x) (.f64 y y))) (.f64 y y)) (*.f64 y y))
▶	0.2b	(fma.f64 (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 y y))) (.f64 1 (hypot.f64 (.f64 y (sqrt.f64 2)) x)) (.f64 y y))
✓	0.2b	(fma.f64 (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 y y))) (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 y y))) (*.f64 y y))
	1.0b	(+.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 2 (.f64 y y) (.f64 x x))) (cbrt.f64 (fma.f64 2 (.f64 y y) (.f64 x x)))) (cbrt.f64 (fma.f64 2 (.f64 y y) (.f64 x x)))) (*.f64 y y))
	0.3b	(.f64 (sqrt.f64 (fma.f64 y (.f64 y 3) (.f64 x x))) (sqrt.f64 (fma.f64 y (.f64 y 3) (*.f64 x x))))

Compiler

Compiled 9063 to 2000 computations (77.9% saved)

localize13.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 y y))
✓	0.2b	(fma.f64 (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 y y))) (.f64 1 (hypot.f64 (.f64 y (sqrt.f64 2)) x)) (.f64 y y))
✓	0.4b	(*.f64 y (sqrt.f64 2))
	6.0b	(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 y y)))

series102.0ms (3.9%)

Counts

2 → 24

Calls

2 calls:

98.0ms	(fma.f64 (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 y y))) (.f64 1 (hypot.f64 (.f64 y (sqrt.f64 2)) x)) (.f64 y y))
3.0ms	(*.f64 y (sqrt.f64 2))

rewrite10.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`add-sqr-sqrt_binary64`
6×	`associate-r_binary64`
5×	`*-un-lft-identity_binary64`
5×	`add-cube-cbrt_binary64`
4×	`sqrt-prod_binary64`

Counts

2 → 34

Calls

2 calls:

8.0ms	(*.f64 y (sqrt.f64 2))
0.0ms	(fma.f64 (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 y y))) (.f64 1 (hypot.f64 (.f64 y (sqrt.f64 2)) x)) (.f64 y y))

simplify82.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

489×	`fma-def_binary64`
448×	`associate-l_binary64`
416×	`associate-r_binary64`
321×	`exp-prod_binary64`
287×	`times-frac_binary64`

Counts

58 → 53

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	112	959
1	267	803
2	811	723
3	4511	582
4	4888	582
5	5030	582

prune129.0ms (5%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	141	2	143
Fresh	3	1	4
Picked	0	1	1
Done	1	1	2
Total	145	5	150

Error

0.0b

Counts

150 → 5

Alt Table

Status	Error	Program
✓	0.2b	(fma.f64 (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 y y))) (.f64 1 (hypot.f64 (.f64 y (sqrt.f64 2)) x)) (.f64 y y))
	0.2b	(fma.f64 (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 y y))) (.f64 1 (hypot.f64 (.f64 (.f64 y (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2))) x)) (*.f64 y y))
	0.5b	(fma.f64 (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 y y))) (.f64 1 (hypot.f64 (.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 y) (sqrt.f64 2))) x)) (.f64 y y))
✓	0.1b	(fma.f64 y (.f64 y 3) (.f64 x x))
	0.3b	(.f64 (sqrt.f64 (fma.f64 y (.f64 y 3) (.f64 x x))) (sqrt.f64 (fma.f64 y (.f64 y 3) (*.f64 x x))))

Compiler

Compiled 4362 to 2062 computations (52.7% saved)

regimes853.0ms (32.8%)

Accuracy

Total 0.1b remaining (90.9%)

Threshold costs 0.1b (90.9%)

Counts

166 → 1

Compiler

Compiled 20301 to 10509 computations (48.2% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	19
1	12	19
2	12	19

end0.0ms (0%)

Compiler: Compiled 15 to 8 computations (46.7% saved)

sample637.0ms (24.5%)

Algorithm

1×

intervals

Results

354.0ms	8000×	body	128	valid
0.0ms	9×	body	128	invalid

Compiler

Compiled 156 to 86 computations (44.9% saved)

Details

analyze76.0ms (2.9%)

sample28.0ms (1.1%)

simplify9.0ms (0.3%)

prune3.0ms (0.1%)

localize5.0ms (0.2%)

series7.0ms (0.3%)

rewrite1.0ms (0%)

simplify55.0ms (2.1%)

prune18.0ms (0.7%)

localize8.0ms (0.3%)

series22.0ms (0.9%)

rewrite19.0ms (0.7%)

simplify81.0ms (3.1%)

prune68.0ms (2.6%)

localize7.0ms (0.3%)

series111.0ms (4.3%)

rewrite6.0ms (0.2%)

simplify44.0ms (1.7%)

prune209.0ms (8%)

localize13.0ms (0.5%)

series102.0ms (3.9%)

rewrite10.0ms (0.4%)

simplify82.0ms (3.1%)

prune129.0ms (5%)

regimes853.0ms (32.8%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample637.0ms (24.5%)

Profiling