Details

analyze351.0ms (12.2%)

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
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
12.5%	87.4%	0.1%	7
12.5%	71.8%	15.7%	8
25%	56.2%	18.9%	9
31.2%	43.7%	25.1%	10
39%	34.7%	26.3%	11
44.9%	27.9%	27.3%	12
47.8%	22%	30.2%	13
52.6%	16.8%	30.7%	14

Compiler

Compiled 13 to 9 computations (30.8% saved)

sample934.0ms (32.5%)

Symmetry

(sort y z)

Results

838.0ms	8256×	body	128	valid
43.0ms	470×	body	128	invalid

Compiler

Compiled 38 to 26 computations (31.6% saved)

simplify16.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

335×	`fma-def_binary64`
126×	`fma-neg_binary64`
61×	`cancel-sign-sub-inv_binary64`
40×	`distribute-rgt-neg-in_binary64`
28×	`sub-neg_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	19	11
2	50	11
3	107	11
4	163	11
5	235	11
6	342	11
7	441	11
8	586	11
9	834	11
10	934	11
11	946	11

Stop Event

1×

saturated

Counts

1 → 2

prune6.0ms (0.2%)

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

0.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.0b	(fma.f64 x x (.f64 y (.f64 z -4)))

Compiler

Compiled 42 to 26 computations (38.1% saved)

localize5.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x x (.f64 y (.f64 z -4)))

series9.0ms (0.3%)

Counts

1 → 36

Calls

1 calls:

9.0ms

(fma.f64 x x (*.f64 y (*.f64 z -4)))

rewrite47.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

686×	`log1p-expm1-u_binary64`
686×	`expm1-log1p-u_binary64`
165×	`prod-diff_binary64`
144×	`expm1-udef_binary64`
144×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	11
1	160	11
2	1871	11

Stop Event

1×	node limit

Counts

1 → 23

Calls

1 calls:

46.0ms

(fma.f64 x x (*.f64 y (*.f64 z -4)))

simplify36.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

456×	`cancel-sign-sub-inv_binary64`
434×	`unswap-sqr_binary64`
365×	`fma-def_binary64`
327×	`fma-neg_binary64`
296×	`distribute-rgt-neg-in_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	402
1	28	348
2	66	348
3	136	348
4	222	348
5	461	348
6	1380	348
7	3403	348

Stop Event

1×	node limit

Counts

59 → 29

prune17.0ms (0.6%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	28	1	29
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	28	2	30

Error

Counts

30 → 2

Alt Table

Status	Error	Program
✓	0.0b	(fma.f64 x x (.f64 y (.f64 z -4)))
▶	1.3b	(pow.f64 (cbrt.f64 (fma.f64 x x (.f64 y (.f64 z -4)))) 3)

Compiler

Compiled 388 to 231 computations (40.5% saved)

localize9.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(fma.f64 x x (.f64 y (.f64 z -4)))
✓	0.7b	(pow.f64 (cbrt.f64 (fma.f64 x x (.f64 y (.f64 z -4)))) 3)
✓	2.7b	(cbrt.f64 (fma.f64 x x (.f64 y (.f64 z -4))))

series1.1s (37.9%)

Counts

2 → 72

Calls

2 calls:

1.0s	(pow.f64 (cbrt.f64 (fma.f64 x x (.f64 y (.f64 z -4)))) 3)
41.0ms	(cbrt.f64 (fma.f64 x x (.f64 y (.f64 z -4))))

rewrite45.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

853×	`log1p-expm1-u_binary64`
853×	`expm1-log1p-u_binary64`
165×	`prod-diff_binary64`
99×	`add-sqr-sqrt_binary64`
93×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	24
1	221	24
2	2371	24

Stop Event

1×	node limit

Counts

2 → 49

Calls

2 calls:

43.0ms	(pow.f64 (cbrt.f64 (fma.f64 x x (.f64 y (.f64 z -4)))) 3)
43.0ms	(cbrt.f64 (fma.f64 x x (.f64 y (.f64 z -4))))

simplify62.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

560×	`fma-def_binary64`
445×	`cancel-sign-sub-inv_binary64`
222×	`distribute-neg-frac_binary64`
221×	`unswap-sqr_binary64`
166×	`associate-r_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	195	3062
1	672	2955
2	2695	2845

Stop Event

1×	node limit

Counts

121 → 121

prune90.0ms (3.1%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	150	0	150
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	150	2	152

Error

Counts

152 → 2

Alt Table

Status	Error	Program
✓	0.0b	(fma.f64 x x (.f64 y (.f64 z -4)))
✓	1.3b	(pow.f64 (cbrt.f64 (fma.f64 x x (.f64 y (.f64 z -4)))) 3)

Compiler

Compiled 3861 to 2744 computations (28.9% saved)

regimes111.0ms (3.9%)

Accuracy

Total 0.0b remaining (2.2%)

Threshold costs 0.0b (2.2%)

Counts

11 → 1

Compiler

Compiled 998 to 753 computations (24.5% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	11
1	10	11

Stop Event

1×

saturated

end47.0ms (1.6%)

Remove: (sort y z)
Compiler: Compiled 69 to 45 computations (34.8% saved)

Iter	Nodes	Cost
0	9	13
1	19	11
2	50	11
3	107	11
4	163	11
5	235	11
6	342	11
7	441	11
8	586	11
9	834	11
10	934	11
11	946	11

Iter	Nodes	Cost
0	9	13
1	19	11
2	50	11
3	107	11
4	163	11
5	235	11
6	342	11
7	441	11
8	586	11
9	834	11
10	934	11
11	946	11

Details

analyze351.0ms (12.2%)

sample934.0ms (32.5%)

simplify16.0ms (0.6%)

prune6.0ms (0.2%)

localize5.0ms (0.2%)

series9.0ms (0.3%)

rewrite47.0ms (1.6%)

simplify36.0ms (1.2%)

prune17.0ms (0.6%)

localize9.0ms (0.3%)

series1.1s (37.9%)

rewrite45.0ms (1.6%)

simplify62.0ms (2.1%)

prune90.0ms (3.1%)

regimes111.0ms (3.9%)

simplify2.0ms (0.1%)

end47.0ms (1.6%)

Profiling

Iter	Nodes	Cost
0	9	13
1	19	11
2	50	11
3	107	11
4	163	11
5	235	11
6	342	11
7	441	11
8	586	11
9	834	11
10	934	11
11	946	11