Details

analyze93.0ms (3.4%)

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)

sample768.0ms (27.9%)

Results

739.0ms	8256×	body	128	valid
1.0ms	9×	body	128	invalid

Compiler

Compiled 53 to 23 computations (56.6% saved)

simplify7.0ms (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)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	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))

series19.0ms (0.7%)

Counts

2 → 48

Calls

2 calls:

10.0ms	(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 y y))
8.0ms	(+.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 y y)) (.f64 y y))

rewrite12.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-log-exp_binary64`
9×	`sum-log_binary64`
6×	`fma-def_binary64`
4×	`*-un-lft-identity_binary64`
4×	`add-sqr-sqrt_binary64`

Counts

2 → 37

Calls

2 calls:

6.0ms	(+.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 y y)) (.f64 y y))
4.0ms	(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 y y))

simplify76.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

520×	`cancel-sign-sub-inv_binary64`
492×	`fma-neg_binary64`
453×	`fma-def_binary64`
414×	`distribute-rgt-out_binary64`
376×	`distribute-rgt-in_binary64`

Counts

85 → 67

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	61	1132
1	186	1028
2	588	941
3	2530	937
4	4456	937
5	4891	937

prune50.0ms (1.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	63	4	67
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	63	6	69

Error

Counts

69 → 6

Alt Table

Status	Error	Program
▶	0.1b	(fma.f64 y (.f64 y 3) (.f64 x x))
	45.9b	(/.f64 (+.f64 (pow.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 y y)) 3) (pow.f64 (.f64 y y) 3)) (+.f64 (.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 y y)) (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 y y))) (-.f64 (.f64 (.f64 y y) (.f64 y y)) (.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 y y)) (*.f64 y y)))))
✓	0.1b	(+.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 y y)) (.f64 y y))
	0.3b	(.f64 (sqrt.f64 (+.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 y y)) (.f64 y y))) (sqrt.f64 (+.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 y y)) (*.f64 y y))))
	1.3b	(.f64 (.f64 (cbrt.f64 (fma.f64 3 (.f64 y y) (.f64 x x))) (cbrt.f64 (fma.f64 3 (.f64 y y) (.f64 x x)))) (cbrt.f64 (fma.f64 3 (.f64 y y) (.f64 x x))))
	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))

Compiler

Compiled 1768 to 400 computations (77.4% 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))

simplify57.0ms (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

prune24.0ms (0.9%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	23	1	24
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	24	6	30

Error

Counts

30 → 6

Alt Table

Status	Error	Program
	0.3b	(.f64 (sqrt.f64 (fma.f64 x x (.f64 3 (.f64 y y)))) (sqrt.f64 (fma.f64 x x (.f64 3 (*.f64 y y)))))
✓	0.1b	(fma.f64 y (.f64 y 3) (.f64 x x))
	45.9b	(/.f64 (+.f64 (pow.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 y y)) 3) (pow.f64 (.f64 y y) 3)) (+.f64 (.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 y y)) (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 y y))) (-.f64 (.f64 (.f64 y y) (.f64 y y)) (.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 y y)) (*.f64 y y)))))
✓	0.1b	(+.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 y y)) (.f64 y y))
	1.3b	(.f64 (.f64 (cbrt.f64 (fma.f64 3 (.f64 y y) (.f64 x x))) (cbrt.f64 (fma.f64 3 (.f64 y y) (.f64 x x)))) (cbrt.f64 (fma.f64 3 (.f64 y y) (.f64 x x))))
▶	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))

Compiler

Compiled 616 to 260 computations (57.8% saved)

localize7.0ms (0.3%)

Local error

Found 3 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))) (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 y y))) (*.f64 y y))
✓	5.7b	(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 y y)))

series139.0ms (5.1%)

Counts

2 → 48

Calls

2 calls:

125.0ms

(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))

14.0ms

(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))

simplify48.0ms (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

prune170.0ms (6.2%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	204	2	206
Fresh	3	0	3
Picked	0	1	1
Done	0	2	2
Total	207	5	212

Error

Counts

212 → 5

Alt Table

Status	Error	Program
	0.7b	(fma.f64 (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 y y))) (.f64 (fabs.f64 (cbrt.f64 (fma.f64 2 (.f64 y y) (.f64 x x)))) (sqrt.f64 (cbrt.f64 (fma.f64 2 (.f64 y y) (.f64 x x))))) (*.f64 y y))
✓	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))
▶	0.5b	(fma.f64 (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 y y))) (.f64 (sqrt.f64 (hypot.f64 (.f64 y (sqrt.f64 2)) x)) (sqrt.f64 (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))

Compiler

Compiled 7084 to 1709 computations (75.9% saved)

localize13.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(fma.f64 (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 y y))) (.f64 (sqrt.f64 (hypot.f64 (.f64 y (sqrt.f64 2)) x)) (sqrt.f64 (hypot.f64 (.f64 y (sqrt.f64 2)) x))) (*.f64 y y))
✓	0.5b	(*.f64 y (sqrt.f64 2))
✓	0.6b	(.f64 (sqrt.f64 (hypot.f64 (.f64 y (sqrt.f64 2)) x)) (sqrt.f64 (hypot.f64 (*.f64 y (sqrt.f64 2)) x)))
	5.7b	(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 y y)))

series127.0ms (4.6%)

Counts

3 → 48

Calls

3 calls:

102.0ms

(fma.f64 (sqrt.f64 (+.f64 (+.f64 (*.f64 x x) (*.f64 y y)) (*.f64 y y))) (*.f64 (sqrt.f64 (hypot.f64 (*.f64 y (sqrt.f64 2)) x)) (sqrt.f64 (hypot.f64 (*.f64 y (sqrt.f64 2)) x))) (*.f64 y y))

21.0ms

(*.f64 (sqrt.f64 (hypot.f64 (*.f64 y (sqrt.f64 2)) x)) (sqrt.f64 (hypot.f64 (*.f64 y (sqrt.f64 2)) x)))

3.0ms

(*.f64 y (sqrt.f64 2))

rewrite15.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

34×	`add-sqr-sqrt_binary64`
22×	`sqrt-prod_binary64`
20×	`pow1_binary64`
14×	`*-un-lft-identity_binary64`
14×	`add-cube-cbrt_binary64`

Counts

3 → 87

Calls

3 calls:

5.0ms

(*.f64 (sqrt.f64 (hypot.f64 (*.f64 y (sqrt.f64 2)) x)) (sqrt.f64 (hypot.f64 (*.f64 y (sqrt.f64 2)) x)))

3.0ms

(*.f64 y (sqrt.f64 2))

0.0ms

(fma.f64 (sqrt.f64 (+.f64 (+.f64 (*.f64 x x) (*.f64 y y)) (*.f64 y y))) (*.f64 (sqrt.f64 (hypot.f64 (*.f64 y (sqrt.f64 2)) x)) (sqrt.f64 (hypot.f64 (*.f64 y (sqrt.f64 2)) x))) (*.f64 y y))

simplify71.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

711×	`fma-def_binary64`
658×	`associate-/l*_binary64`
601×	`associate-/r*_binary64`
238×	`cancel-sign-sub-inv_binary64`
140×	`fma-neg_binary64`

Counts

135 → 147

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	193	3063
1	477	2564
2	1569	2229
3	5128	2229

prune246.0ms (8.9%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	229	0	229
Fresh	0	1	1
Picked	0	1	1
Done	0	3	3
Total	229	5	234

Error

Counts

234 → 5

Alt Table

Status	Error	Program
	0.7b	(fma.f64 (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 y y))) (.f64 (fabs.f64 (cbrt.f64 (fma.f64 2 (.f64 y y) (.f64 x x)))) (sqrt.f64 (cbrt.f64 (fma.f64 2 (.f64 y y) (.f64 x x))))) (*.f64 y y))
✓	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))
✓	0.5b	(fma.f64 (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 y y))) (.f64 (sqrt.f64 (hypot.f64 (.f64 y (sqrt.f64 2)) x)) (sqrt.f64 (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))

Compiler

Compiled 8422 to 4174 computations (50.4% saved)

regimes708.0ms (25.7%)

Accuracy

Total 0.1b remaining (90.3%)

Threshold costs 0.1b (90.3%)

Counts

125 → 1

Compiler

Compiled 18901 to 10175 computations (46.2% 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	10	19
1	13	19
2	13	19

end76.0ms (2.8%)

Compiler: Compiled 159 to 79 computations (50.3% saved)

Details

analyze93.0ms (3.4%)

sample768.0ms (27.9%)

simplify7.0ms (0.3%)

prune3.0ms (0.1%)

localize6.0ms (0.2%)

series19.0ms (0.7%)

rewrite12.0ms (0.5%)

simplify76.0ms (2.8%)

prune50.0ms (1.8%)

localize5.0ms (0.2%)

series7.0ms (0.3%)

rewrite1.0ms (0%)

simplify57.0ms (2.1%)

prune24.0ms (0.9%)

localize7.0ms (0.3%)

series139.0ms (5.1%)

rewrite6.0ms (0.2%)

simplify48.0ms (1.7%)

prune170.0ms (6.2%)

localize13.0ms (0.5%)

series127.0ms (4.6%)

rewrite15.0ms (0.5%)

simplify71.0ms (2.6%)

prune246.0ms (8.9%)

regimes708.0ms (25.7%)

simplify2.0ms (0.1%)

end76.0ms (2.8%)

Profiling