Details

analyze1.0ms (0.1%)

Algorithm

1×

Search

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

Compiler

Compiled 14 to 11 computations (21.4% saved)

sample685.0ms (39.6%)

Infinites

11.9% of outputs are infinite.

Results

557.0ms

8256×

body

128

valid

Compiler

Compiled 41 to 32 computations (22% saved)

simplify46.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

723×	`fma-neg_binary64`
586×	`fma-def_binary64`
222×	`cancel-sign-sub-inv_binary64`
115×	`sub-neg_binary64`
82×	`associate--r+_binary64`

Counts

1 → 2

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	11	16
1	27	14
2	58	12
3	109	12
4	229	11
5	450	11
6	661	11
7	940	11
8	1194	11
9	1320	11
10	1347	11
11	1268	11

prune3.0ms (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

0.0b

Counts

3 → 2

Alt Table

Status	Error	Program
	0.0b	(-.f64 (fma.f64 y (+.f64 x -1/2) 918938533204673/1000000000000000) x)
▶	0.0b	(+.f64 (-.f64 (.f64 x (-.f64 y 1)) (.f64 y 1/2)) 918938533204673/1000000000000000)

Compiler

Compiled 67 to 49 computations (26.9% saved)

localize6.0ms (0.4%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (-.f64 (.f64 x (-.f64 y 1)) (.f64 y 1/2)) 918938533204673/1000000000000000)
✓	0.0b	(*.f64 x (-.f64 y 1))

series10.0ms (0.6%)

Counts

2 → 48

Calls

2 calls:

5.0ms	(+.f64 (-.f64 (.f64 x (-.f64 y 1)) (.f64 y 1/2)) 918938533204673/1000000000000000)
4.0ms	(*.f64 x (-.f64 y 1))

rewrite25.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

39×	`add-sqr-sqrt_binary64`
38×	`*-un-lft-identity_binary64`
37×	`prod-diff_binary64`
33×	`add-cube-cbrt_binary64`
29×	`associate-+l+_binary64`

Counts

2 → 100

Calls

2 calls:

11.0ms	(+.f64 (-.f64 (.f64 x (-.f64 y 1)) (.f64 y 1/2)) 918938533204673/1000000000000000)
6.0ms	(*.f64 x (-.f64 y 1))

simplify91.0ms (5.3%)

Algorithm

1×	egg-herbie

Rules

600×	`fma-neg_binary64`
323×	`associate-l_binary64`
298×	`exp-prod_binary64`
270×	`associate-r_binary64`
265×	`cancel-sign-sub-inv_binary64`

Counts

148 → 159

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	135	1505
1	282	1324
2	696	1275
3	2422	1244
4	4328	1244
5	5057	1244

prune133.0ms (7.7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	157	2	159
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	158	3	161

Error

Counts

161 → 3

Alt Table

Status	Error	Program
▶	0.0b	(+.f64 (*.f64 y x) (-.f64 918938533204673/1000000000000000 (fma.f64 y 1/2 x)))
	30.1b	(cbrt.f64 (.f64 (.f64 (+.f64 (-.f64 (.f64 x (-.f64 y 1)) (.f64 y 1/2)) 918938533204673/1000000000000000) (+.f64 (-.f64 (.f64 x (-.f64 y 1)) (.f64 y 1/2)) 918938533204673/1000000000000000)) (+.f64 (-.f64 (.f64 x (-.f64 y 1)) (.f64 y 1/2)) 918938533204673/1000000000000000)))
✓	0.0b	(+.f64 (-.f64 (.f64 x (-.f64 y 1)) (.f64 y 1/2)) 918938533204673/1000000000000000)

Compiler

Compiled 3360 to 2498 computations (25.7% saved)

localize6.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 918938533204673/1000000000000000 (fma.f64 y 1/2 x))
✓	0.0b	(+.f64 (*.f64 y x) (-.f64 918938533204673/1000000000000000 (fma.f64 y 1/2 x)))

series9.0ms (0.5%)

Counts

2 → 48

Calls

2 calls:

5.0ms	(+.f64 (*.f64 y x) (-.f64 918938533204673/1000000000000000 (fma.f64 y 1/2 x)))
4.0ms	(-.f64 918938533204673/1000000000000000 (fma.f64 y 1/2 x))

rewrite15.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`*-un-lft-identity_binary64`
19×	`add-sqr-sqrt_binary64`
18×	`prod-diff_binary64`
17×	`add-cube-cbrt_binary64`
13×	`associate-+r+_binary64`

Counts

2 → 60

Calls

2 calls:

8.0ms	(+.f64 (*.f64 y x) (-.f64 918938533204673/1000000000000000 (fma.f64 y 1/2 x)))
3.0ms	(-.f64 918938533204673/1000000000000000 (fma.f64 y 1/2 x))

simplify92.0ms (5.3%)

Algorithm

1×	egg-herbie

Rules

950×	`fma-neg_binary64`
447×	`distribute-rgt-in_binary64`
443×	`fma-def_binary64`
437×	`associate-l_binary64`
427×	`distribute-lft-in_binary64`

Counts

108 → 102

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	122	1300
1	256	1213
2	795	1144
3	3604	1142
4	4317	1142
5	4816	1142

prune102.0ms (5.9%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	101	1	102
Fresh	1	0	1
Picked	1	0	1
Done	0	1	1
Total	103	2	105

Error

Counts

105 → 2

Alt Table

Status	Error	Program
▶	0.0b	(+.f64 (.f64 y x) (fma.f64 (.f64 (cbrt.f64 918938533204673/1000000000000000) (cbrt.f64 918938533204673/1000000000000000)) (cbrt.f64 918938533204673/1000000000000000) (neg.f64 (fma.f64 y 1/2 x))))
✓	0.0b	(+.f64 (-.f64 (.f64 x (-.f64 y 1)) (.f64 y 1/2)) 918938533204673/1000000000000000)

Status

Error

Program

▶

0.0b

(+.f64 (*.f64 y x) (fma.f64 (*.f64 (cbrt.f64 918938533204673/1000000000000000) (cbrt.f64 918938533204673/1000000000000000)) (cbrt.f64 918938533204673/1000000000000000) (neg.f64 (fma.f64 y 1/2 x))))

✓

0.0b

(+.f64 (-.f64 (*.f64 x (-.f64 y 1)) (*.f64 y 1/2)) 918938533204673/1000000000000000)

Compiler

Compiled 2215 to 1411 computations (36.3% saved)

localize11.0ms (0.6%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 y x) (fma.f64 (.f64 (cbrt.f64 918938533204673/1000000000000000) (cbrt.f64 918938533204673/1000000000000000)) (cbrt.f64 918938533204673/1000000000000000) (neg.f64 (fma.f64 y 1/2 x))))

series22.0ms (1.3%)

Counts

1 → 24

Calls

1 calls:

22.0ms

(+.f64 (*.f64 y x) (fma.f64 (*.f64 (cbrt.f64 918938533204673/1000000000000000) (cbrt.f64 918938533204673/1000000000000000)) (cbrt.f64 918938533204673/1000000000000000) (neg.f64 (fma.f64 y 1/2 x))))

rewrite6.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`add-log-exp_binary64`
1×	`+-commutative_binary64`
1×	`associate-+r+_binary64`
1×	`fma-udef_binary64`
1×	`flip-+_binary64`

Counts

1 → 15

Calls

1 calls:

5.0ms

(+.f64 (*.f64 y x) (fma.f64 (*.f64 (cbrt.f64 918938533204673/1000000000000000) (cbrt.f64 918938533204673/1000000000000000)) (cbrt.f64 918938533204673/1000000000000000) (neg.f64 (fma.f64 y 1/2 x))))

simplify79.0ms (4.5%)

Algorithm

1×	egg-herbie

Rules

739×	`associate-+l+_binary64`
412×	`unsub-neg_binary64`
395×	`neg-mul-1_binary64`
306×	`sub-neg_binary64`
287×	`distribute-neg-in_binary64`

Counts

39 → 36

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	55	576
1	161	513
2	447	507
3	1656	505
4	3479	505
5	4650	505
6	4941	505

prune27.0ms (1.6%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	36	0	36
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	36	2	38

Error

Counts

38 → 2

Alt Table

Status	Error	Program
✓	0.0b	(+.f64 (.f64 y x) (fma.f64 (.f64 (cbrt.f64 918938533204673/1000000000000000) (cbrt.f64 918938533204673/1000000000000000)) (cbrt.f64 918938533204673/1000000000000000) (neg.f64 (fma.f64 y 1/2 x))))
✓	0.0b	(+.f64 (-.f64 (.f64 x (-.f64 y 1)) (.f64 y 1/2)) 918938533204673/1000000000000000)

Status

Error

Program

✓

0.0b

(+.f64 (*.f64 y x) (fma.f64 (*.f64 (cbrt.f64 918938533204673/1000000000000000) (cbrt.f64 918938533204673/1000000000000000)) (cbrt.f64 918938533204673/1000000000000000) (neg.f64 (fma.f64 y 1/2 x))))

✓

0.0b

(+.f64 (-.f64 (*.f64 x (-.f64 y 1)) (*.f64 y 1/2)) 918938533204673/1000000000000000)

Compiler

Compiled 746 to 519 computations (30.4% saved)

regimes256.0ms (14.8%)

Accuracy

Total -0.0b remaining (-158.3%)

Threshold costs -0.0b (-158.3%)

Counts

60 → 1

Compiler

Compiled 4076 to 2884 computations (29.2% saved)

simplify4.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`
1×	`*-commutative_binary64`
1×	`sub-neg_binary64`
1×	`neg-sub0_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	24
1	15	24
2	17	24
3	18	24
4	18	24

end99.0ms (5.7%)

Compiler: Compiled 68 to 53 computations (22.1% saved)

Details

analyze1.0ms (0.1%)

sample685.0ms (39.6%)

simplify46.0ms (2.7%)

prune3.0ms (0.2%)

localize6.0ms (0.4%)

series10.0ms (0.6%)

rewrite25.0ms (1.4%)

simplify91.0ms (5.3%)

prune133.0ms (7.7%)

localize6.0ms (0.3%)

series9.0ms (0.5%)

rewrite15.0ms (0.8%)

simplify92.0ms (5.3%)

prune102.0ms (5.9%)

localize11.0ms (0.6%)

series22.0ms (1.3%)

rewrite6.0ms (0.3%)

simplify79.0ms (4.5%)

prune27.0ms (1.6%)

regimes256.0ms (14.8%)

simplify4.0ms (0.2%)

end99.0ms (5.7%)

Profiling