Details

analyze14.0ms (0.7%)

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
25%	74.9%	0.1%	6
93.7%	6.2%	0.1%	7
96.8%	3.1%	0.1%	8
99.5%	0.4%	0.1%	9
99.7%	0.2%	0.1%	10
99.8%	0.1%	0.1%	11
99.9%	0%	0.1%	12
99.9%	0%	0.1%	13
99.9%	0%	0.1%	14

Compiler

Compiled 22 to 13 computations (40.9% saved)

sample1.1s (51.6%)

Results

917.0ms

8256×

body

128

valid

Compiler

Compiled 65 to 38 computations (41.5% saved)

simplify113.0ms (5.5%)

Algorithm

1×	egg-herbie

Rules

620×	`fma-def_binary64`
549×	`sub-neg_binary64`
460×	`distribute-neg-frac_binary64`
455×	`cancel-sign-sub-inv_binary64`
430×	`times-frac_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	26
1	23	24
2	52	24
3	105	24
4	199	24
5	330	24
6	442	24
7	603	24
8	901	24
9	2304	24
10	3386	24
11	3956	24
12	4454	24
13	4735	24
14	5238	24

prune3.0ms (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

30.5b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	30.5b	(/.f64 (fma.f64 -4 (.f64 y y) (.f64 x x)) (fma.f64 x x (.f64 y (.f64 y 4))))

Compiler

Compiled 76 to 42 computations (44.7% saved)

localize9.0ms (0.5%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	4.2b	(fma.f64 -4 (.f64 y y) (.f64 x x))
✓	29.9b	(/.f64 (fma.f64 -4 (.f64 y y) (.f64 x x)) (fma.f64 x x (.f64 y (.f64 y 4))))

series28.0ms (1.4%)

Counts

2 → 48

Calls

2 calls:

20.0ms	(/.f64 (fma.f64 -4 (.f64 y y) (.f64 x x)) (fma.f64 x x (.f64 y (.f64 y 4))))
9.0ms	(fma.f64 -4 (.f64 y y) (.f64 x x))

rewrite4.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`*-un-lft-identity_binary64`
10×	`add-sqr-sqrt_binary64`
10×	`add-cube-cbrt_binary64`
9×	`times-frac_binary64`
4×	`add-cbrt-cube_binary64`

Counts

2 → 39

Calls

2 calls:

2.0ms	(/.f64 (fma.f64 -4 (.f64 y y) (.f64 x x)) (fma.f64 x x (.f64 y (.f64 y 4))))
0.0ms	(fma.f64 -4 (.f64 y y) (.f64 x x))

simplify92.0ms (4.4%)

Algorithm

1×	egg-herbie

Rules

623×	`fma-def_binary64`
491×	`div-sub_binary64`
392×	`fma-neg_binary64`
350×	`cancel-sign-sub-inv_binary64`
219×	`distribute-rgt-in_binary64`

Counts

87 → 90

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	104	2105
1	216	1928
2	563	1916
3	2054	1898
4	4435	1862
5	5400	1862

prune64.0ms (3.1%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	85	5	90
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	86	5	91

Error

0.2b

Counts

91 → 5

Alt Table

Status	Error	Program
	30.5b	(expm1.f64 (log1p.f64 (/.f64 (fma.f64 y (.f64 y -4) (.f64 x x)) (fma.f64 y (.f64 y 4) (.f64 x x)))))
	37.3b	(fma.f64 1/2 (/.f64 (.f64 x x) (.f64 y y)) -1)
	33.4b	-1
	34.4b	(fma.f64 (/.f64 (.f64 y y) (.f64 x x)) -8 1)
▶	30.4b	1

Compiler

Compiled 2485 to 1255 computations (49.5% saved)

localize0.0ms (0%)

prune4.0ms (0.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Kept	Total
New	0	0
Fresh	4	4
Picked	1	1
Done	0	0
Total	5	5

Error

0.2b

Counts

5 → 5

Alt Table

Status	Error	Program
▶	30.5b	(expm1.f64 (log1p.f64 (/.f64 (fma.f64 y (.f64 y -4) (.f64 x x)) (fma.f64 y (.f64 y 4) (.f64 x x)))))
	37.3b	(fma.f64 1/2 (/.f64 (.f64 x x) (.f64 y y)) -1)
	33.4b	-1
	34.4b	(fma.f64 (/.f64 (.f64 y y) (.f64 x x)) -8 1)
✓	30.4b	1

Compiler

Compiled 99 to 65 computations (34.3% saved)

localize11.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 y (.f64 y 4) (.f64 x x))
✓	2.2b	(log1p.f64 (/.f64 (fma.f64 y (.f64 y -4) (.f64 x x)) (fma.f64 y (.f64 y 4) (.f64 x x))))
✓	2.7b	(fma.f64 y (.f64 y -4) (.f64 x x))
✓	29.9b	(/.f64 (fma.f64 y (.f64 y -4) (.f64 x x)) (fma.f64 y (.f64 y 4) (.f64 x x)))

series77.0ms (3.7%)

Counts

4 → 96

Calls

4 calls:

39.0ms	(log1p.f64 (/.f64 (fma.f64 y (.f64 y -4) (.f64 x x)) (fma.f64 y (.f64 y 4) (.f64 x x))))
22.0ms	(/.f64 (fma.f64 y (.f64 y -4) (.f64 x x)) (fma.f64 y (.f64 y 4) (.f64 x x)))
9.0ms	(fma.f64 y (.f64 y 4) (.f64 x x))
7.0ms	(fma.f64 y (.f64 y -4) (.f64 x x))

rewrite6.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`*-un-lft-identity_binary64`
12×	`add-sqr-sqrt_binary64`
12×	`add-cube-cbrt_binary64`
9×	`times-frac_binary64`
6×	`add-cbrt-cube_binary64`

Counts

4 → 60

Calls

4 calls:

2.0ms	(/.f64 (fma.f64 y (.f64 y -4) (.f64 x x)) (fma.f64 y (.f64 y 4) (.f64 x x)))
0.0ms	(fma.f64 y (.f64 y 4) (.f64 x x))
0.0ms	(log1p.f64 (/.f64 (fma.f64 y (.f64 y -4) (.f64 x x)) (fma.f64 y (.f64 y 4) (.f64 x x))))
0.0ms	(fma.f64 y (.f64 y -4) (.f64 x x))

simplify141.0ms (6.8%)

Algorithm

1×	egg-herbie

Rules

723×	`fma-neg_binary64`
282×	`fma-def_binary64`
220×	`times-frac_binary64`
200×	`cancel-sign-sub-inv_binary64`
171×	`associate-/l*_binary64`

Counts

156 → 152

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	163	3634
1	387	3353
2	1056	3301
3	3863	3289
4	4953	3289
5	5000	3289
6	4944	3289

prune95.0ms (4.6%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	152	0	152
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	152	5	157

Error

0.2b

Counts

157 → 5

Alt Table

Status	Error	Program
✓	30.5b	(expm1.f64 (log1p.f64 (/.f64 (fma.f64 y (.f64 y -4) (.f64 x x)) (fma.f64 y (.f64 y 4) (.f64 x x)))))
	37.3b	(fma.f64 1/2 (/.f64 (.f64 x x) (.f64 y y)) -1)
▶	33.4b	-1
	34.4b	(fma.f64 (/.f64 (.f64 y y) (.f64 x x)) -8 1)
✓	30.4b	1

Compiler

Compiled 4248 to 2325 computations (45.3% saved)

localize0.0ms (0%)

prune3.0ms (0.1%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Kept	Total
New	0	0
Fresh	2	2
Picked	1	1
Done	2	2
Total	5	5

Error

0.2b

Counts

5 → 5

Alt Table

Status	Error	Program
✓	30.5b	(expm1.f64 (log1p.f64 (/.f64 (fma.f64 y (.f64 y -4) (.f64 x x)) (fma.f64 y (.f64 y 4) (.f64 x x)))))
	37.3b	(fma.f64 1/2 (/.f64 (.f64 x x) (.f64 y y)) -1)
✓	33.4b	-1
	34.4b	(fma.f64 (/.f64 (.f64 y y) (.f64 x x)) -8 1)
✓	30.4b	1

Compiler

Compiled 51 to 34 computations (33.3% saved)

regimes177.0ms (8.5%)

Accuracy

Total 12.1b remaining (97.2%)

Threshold costs 0b (0%)

Counts

14 → 5

Compiler

Compiled 1373 to 923 computations (32.8% saved)

bsearch82.0ms (3.9%)

Steps

Iters	Range		Point
10	3.223565668612699e+139	1.4578059490587685e+156	9.896373077841149e+151
10	3.694355653499463e-74	8.119864010891657e-63	1.733125606425097e-69
7	-1.687074980602566e-66	-4.167470410789706e-68	-5.472397692701883e-68
8	-1.6140196013183496e+156	-4.547171617256569e+151	-4.624630821563891e+151

Compiler

Compiled 3 to 2 computations (33.3% saved)

simplify3.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	79
1	38	79
2	37	79

end77.0ms (3.7%)

Compiler: Compiled 165 to 104 computations (37% saved)

Details

analyze14.0ms (0.7%)

sample1.1s (51.6%)

simplify113.0ms (5.5%)

prune3.0ms (0.2%)

localize9.0ms (0.5%)

series28.0ms (1.4%)

rewrite4.0ms (0.2%)

simplify92.0ms (4.4%)

prune64.0ms (3.1%)

localize0.0ms (0%)

prune4.0ms (0.2%)

localize11.0ms (0.5%)

series77.0ms (3.7%)

rewrite6.0ms (0.3%)

simplify141.0ms (6.8%)

prune95.0ms (4.6%)

localize0.0ms (0%)

prune3.0ms (0.1%)

regimes177.0ms (8.5%)

bsearch82.0ms (3.9%)

simplify3.0ms (0.2%)

end77.0ms (3.7%)

Profiling