Details

analyze1.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
99.9%	0%	0.1%	1

Compiler

Compiled 32 to 20 computations (37.5% saved)

sample1.1s (35.2%)

Results

997.0ms

8256×

body

128

valid

Compiler

Compiled 95 to 59 computations (37.9% saved)

simplify60.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

620×	`fma-def_binary64`
556×	`cancel-sign-sub-inv_binary64`
552×	`unswap-sqr_binary64`
357×	`unsub-neg_binary64`
344×	`+-commutative_binary64`

Counts

1 → 2

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	19	39
1	57	37
2	168	37
3	492	37
4	1604	33
5	2891	33
6	4309	33
7	5214	33

prune5.0ms (0.2%)

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

14.0b

Counts

3 → 2

Alt Table

Status	Error	Program
	16.3b	(-.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (+.f64 (.f64 (.f64 a a) (-.f64 1 a)) (.f64 (*.f64 b b) (+.f64 3 a))))) 1)
▶	14.0b	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3))) -1))

Status

Error

Program

16.3b

(-.f64 (+.f64 (pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) 2) (*.f64 4 (+.f64 (*.f64 (*.f64 a a) (-.f64 1 a)) (*.f64 (*.f64 b b) (+.f64 3 a))))) 1)

▶

14.0b

(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (fma.f64 (*.f64 a a) (-.f64 1 a) (*.f64 (*.f64 b b) (+.f64 a 3))) -1))

Compiler

Compiled 166 to 104 computations (37.3% saved)

localize16.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3))) -1)
✓	3.2b	(.f64 (.f64 b b) (+.f64 a 3))
✓	4.6b	(fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3)))
✓	9.2b	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3))) -1))

series78.0ms (2.5%)

Counts

4 → 96

Calls

4 calls:

37.0ms	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3))) -1))
18.0ms	(fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3))) -1)
11.0ms	(.f64 (.f64 b b) (+.f64 a 3))
11.0ms	(fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3)))

rewrite16.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`*-un-lft-identity_binary64`
9×	`add-cbrt-cube_binary64`
9×	`add-exp-log_binary64`
9×	`pow1_binary64`
8×	`add-sqr-sqrt_binary64`

Counts

4 → 68

Calls

4 calls:

6.0ms	(.f64 (.f64 b b) (+.f64 a 3))
6.0ms	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3))) -1))
0.0ms	(fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3))) -1)
0.0ms	(fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3)))

simplify104.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

587×	`associate-+l+_binary64`
471×	`distribute-rgt-in_binary64`
461×	`distribute-lft-in_binary64`
383×	`associate--l+_binary64`
273×	`cancel-sign-sub-inv_binary64`

Counts

164 → 163

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	171	3677
1	474	3305
2	1601	3213
3	5204	3213

prune179.0ms (5.8%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	160	3	163
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	161	4	165

Error

Counts

165 → 4

Alt Table

Status	Error	Program
	12.0b	(+.f64 (.f64 (.f64 b b) (+.f64 (+.f64 12 (.f64 b b)) (.f64 a (+.f64 4 (.f64 2 a))))) (fma.f64 4 (.f64 a a) -1))
✓	14.0b	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3))) -1))
▶	0.6b	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 12 (*.f64 b b) -1))
	14.1b	(fma.f64 (sqrt.f64 (pow.f64 (hypot.f64 a b) 4)) (sqrt.f64 (pow.f64 (hypot.f64 a b) 4)) (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3))) -1))

Compiler

Compiled 4826 to 2892 computations (40.1% saved)

localize9.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 12 (*.f64 b b) -1))
✓	0.1b	(fma.f64 12 (*.f64 b b) -1)

series45.0ms (1.5%)

Counts

2 → 36

Calls

2 calls:

42.0ms	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 12 (*.f64 b b) -1))
3.0ms	(fma.f64 12 (*.f64 b b) -1)

rewrite15.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`fma-def_binary64`
6×	`*-un-lft-identity_binary64`
4×	`add-sqr-sqrt_binary64`
4×	`add-cube-cbrt_binary64`
4×	`add-log-exp_binary64`

Counts

2 → 32

Calls

2 calls:

13.0ms	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 12 (*.f64 b b) -1))
0.0ms	(fma.f64 12 (*.f64 b b) -1)

simplify76.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

593×	`associate-+l+_binary64`
545×	`associate-+r+_binary64`
444×	`unsub-neg_binary64`
273×	`fma-def_binary64`
205×	`fma-neg_binary64`

Counts

68 → 64

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	64	1155
1	158	1078
2	452	1012
3	1705	1010
4	4597	1010
5	5142	1010

prune73.0ms (2.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	63	1	64
Fresh	1	1	2
Picked	1	0	1
Done	0	1	1
Total	65	3	68

Error

Counts

68 → 3

Alt Table

Status	Error	Program
▶	0.6b	(+.f64 (fma.f64 12 (*.f64 b b) (pow.f64 (hypot.f64 a b) 4)) -1)
✓	14.0b	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3))) -1))
	14.1b	(fma.f64 (sqrt.f64 (pow.f64 (hypot.f64 a b) 4)) (sqrt.f64 (pow.f64 (hypot.f64 a b) 4)) (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3))) -1))

Compiler

Compiled 1269 to 750 computations (40.9% saved)

localize8.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (fma.f64 12 (*.f64 b b) (pow.f64 (hypot.f64 a b) 4)) -1)
✓	0.1b	(fma.f64 12 (*.f64 b b) (pow.f64 (hypot.f64 a b) 4))

series87.0ms (2.8%)

Counts

2 → 48

Calls

2 calls:

44.0ms	(fma.f64 12 (*.f64 b b) (pow.f64 (hypot.f64 a b) 4))
44.0ms	(+.f64 (fma.f64 12 (*.f64 b b) (pow.f64 (hypot.f64 a b) 4)) -1)

rewrite7.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

5×	`*-un-lft-identity_binary64`
4×	`add-sqr-sqrt_binary64`
4×	`add-log-exp_binary64`
3×	`fma-def_binary64`
3×	`add-cube-cbrt_binary64`

Counts

2 → 29

Calls

2 calls:

6.0ms	(+.f64 (fma.f64 12 (*.f64 b b) (pow.f64 (hypot.f64 a b) 4)) -1)
0.0ms	(fma.f64 12 (*.f64 b b) (pow.f64 (hypot.f64 a b) 4))

simplify80.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

776×	`associate-r_binary64`
652×	`distribute-rgt-in_binary64`
612×	`distribute-lft-in_binary64`
612×	`fma-neg_binary64`
235×	`fma-def_binary64`

Counts

77 → 68

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	65	1702
1	149	1590
2	386	1447
3	1353	1447
4	4870	1447
5	5278	1447

prune68.0ms (2.2%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	68	0	68
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	68	3	71

Error

Counts

71 → 3

Alt Table

Status	Error	Program
✓	0.6b	(+.f64 (fma.f64 12 (*.f64 b b) (pow.f64 (hypot.f64 a b) 4)) -1)
✓	14.0b	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3))) -1))
▶	14.1b	(fma.f64 (sqrt.f64 (pow.f64 (hypot.f64 a b) 4)) (sqrt.f64 (pow.f64 (hypot.f64 a b) 4)) (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3))) -1))

Compiler

Compiled 1441 to 853 computations (40.8% saved)

localize16.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
	3.2b	(.f64 (.f64 b b) (+.f64 a 3))
	4.6b	(fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3)))
✓	9.8b	(fma.f64 (sqrt.f64 (pow.f64 (hypot.f64 a b) 4)) (sqrt.f64 (pow.f64 (hypot.f64 a b) 4)) (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3))) -1))
✓	15.4b	(sqrt.f64 (pow.f64 (hypot.f64 a b) 4))

series104.0ms (3.4%)

Counts

2 → 48

Calls

2 calls:

53.0ms

(sqrt.f64 (pow.f64 (hypot.f64 a b) 4))

51.0ms

(fma.f64 (sqrt.f64 (pow.f64 (hypot.f64 a b) 4)) (sqrt.f64 (pow.f64 (hypot.f64 a b) 4)) (fma.f64 4 (fma.f64 (*.f64 a a) (-.f64 1 a) (*.f64 (*.f64 b b) (+.f64 a 3))) -1))

rewrite3.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`sqrt-prod_binary64`
6×	`add-sqr-sqrt_binary64`
4×	`*-un-lft-identity_binary64`
4×	`unpow-prod-down_binary64`
4×	`add-cube-cbrt_binary64`

Counts

2 → 31

Calls

2 calls:

2.0ms

(sqrt.f64 (pow.f64 (hypot.f64 a b) 4))

0.0ms

(fma.f64 (sqrt.f64 (pow.f64 (hypot.f64 a b) 4)) (sqrt.f64 (pow.f64 (hypot.f64 a b) 4)) (fma.f64 4 (fma.f64 (*.f64 a a) (-.f64 1 a) (*.f64 (*.f64 b b) (+.f64 a 3))) -1))

simplify95.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

627×	`fma-def_binary64`
567×	`fma-neg_binary64`
532×	`cancel-sign-sub-inv_binary64`
512×	`associate-+l+_binary64`
335×	`distribute-lft-out_binary64`

Counts

79 → 80

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	99	1708
1	248	1553
2	746	1322
3	3076	1301
4	4889	1301
5	5008	1301

prune222.0ms (7.2%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	186	0	186
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	186	3	189

Error

Counts

189 → 3

Alt Table

Status	Error	Program
✓	0.6b	(+.f64 (fma.f64 12 (*.f64 b b) (pow.f64 (hypot.f64 a b) 4)) -1)
✓	14.0b	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3))) -1))
✓	14.1b	(fma.f64 (sqrt.f64 (pow.f64 (hypot.f64 a b) 4)) (sqrt.f64 (pow.f64 (hypot.f64 a b) 4)) (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3))) -1))

Compiler

Compiled 6254 to 3591 computations (42.6% saved)

regimes547.0ms (17.8%)

Accuracy

Total 0.5b remaining (98.6%)

Threshold costs 0.5b (98.6%)

Counts

102 → 1

Compiler

Compiled 10089 to 7213 computations (28.5% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	17
1	12	17
2	12	17

end79.0ms (2.6%)

Compiler: Compiled 99 to 68 computations (31.3% saved)

Details

analyze1.0ms (0%)

sample1.1s (35.2%)

simplify60.0ms (1.9%)

prune5.0ms (0.2%)

localize16.0ms (0.5%)

series78.0ms (2.5%)

rewrite16.0ms (0.5%)

simplify104.0ms (3.4%)

prune179.0ms (5.8%)

localize9.0ms (0.3%)

series45.0ms (1.5%)

rewrite15.0ms (0.5%)

simplify76.0ms (2.5%)

prune73.0ms (2.4%)

localize8.0ms (0.2%)

series87.0ms (2.8%)

rewrite7.0ms (0.2%)

simplify80.0ms (2.6%)

prune68.0ms (2.2%)

localize16.0ms (0.5%)

series104.0ms (3.4%)

rewrite3.0ms (0.1%)

simplify95.0ms (3.1%)

prune222.0ms (7.2%)

regimes547.0ms (17.8%)

simplify2.0ms (0.1%)

end79.0ms (2.6%)

Profiling