Details

analyze514.0ms (10.7%)

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
0%	99.9%	0.1%	6
12.5%	87.4%	0.1%	7
18.7%	81.1%	0.1%	8
40.6%	56.9%	2.5%	9
46%	49.5%	4.4%	10
50.3%	44.9%	4.8%	11
60.3%	30.5%	9.2%	12
62.9%	25.7%	11.4%	13
65.2%	23.2%	11.7%	14

Compiler

Compiled 17 to 13 computations (23.5% saved)

sample1.2s (24.2%)

Results

953.0ms	8256×	body	128	valid
120.0ms	997×	body	128	invalid

Compiler

Compiled 50 to 38 computations (24% saved)

simplify62.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

888×	`fma-def_binary64`
639×	`associate-/l*_binary64`
549×	`associate-/r*_binary64`
410×	`fma-neg_binary64`
343×	`distribute-neg-frac_binary64`

Counts

1 → 2

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	13	19
1	25	17
2	55	15
3	125	15
4	273	14
5	562	11
6	1531	11
7	4085	11
8	4535	11
9	4790	11

prune4.0ms (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
▶	0.0b	(fma.f64 4 (/.f64 (-.f64 x z) y) 2)
	0.0b	(+.f64 1 (/.f64 (.f64 4 (-.f64 (+.f64 x (.f64 y 1/4)) z)) y))

Compiler

Compiled 78 to 57 computations (26.9% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 4 (/.f64 (-.f64 x z) y) 2)
✓	0.0b	(/.f64 (-.f64 x z) y)

series28.0ms (0.6%)

Counts

2 → 64

Calls

2 calls:

18.0ms	(fma.f64 4 (/.f64 (-.f64 x z) y) 2)
9.0ms	(/.f64 (-.f64 x z) y)

rewrite7.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`*-un-lft-identity_binary64`
20×	`add-sqr-sqrt_binary64`
15×	`times-frac_binary64`
12×	`add-cube-cbrt_binary64`
5×	`associate-/l*_binary64`

Counts

2 → 50

Calls

2 calls:

5.0ms	(/.f64 (-.f64 x z) y)
0.0ms	(fma.f64 4 (/.f64 (-.f64 x z) y) 2)

simplify170.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

1065×	`div-sub_binary64`
633×	`distribute-rgt-in_binary64`
624×	`distribute-lft-in_binary64`
539×	`times-frac_binary64`
363×	`fma-def_binary64`

Counts

114 → 79

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	107	1334
1	232	1225
2	489	1223
3	1245	1223
4	4609	1223
5	6880	1223

prune150.0ms (3.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	77	2	79
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	78	3	81

Error

Counts

81 → 3

Alt Table

Status	Error	Program
	0.7b	(fma.f64 4 (.f64 (.f64 (cbrt.f64 (/.f64 (-.f64 x z) y)) (cbrt.f64 (/.f64 (-.f64 x z) y))) (cbrt.f64 (/.f64 (-.f64 x z) y))) 2)
▶	0.0b	(fma.f64 4 (-.f64 (/.f64 x y) (/.f64 z y)) 2)
	0.0b	(+.f64 1 (/.f64 (.f64 4 (-.f64 (+.f64 x (.f64 y 1/4)) z)) y))

Compiler

Compiled 1154 to 527 computations (54.3% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 4 (-.f64 (/.f64 x y) (/.f64 z y)) 2)
✓	0.0b	(-.f64 (/.f64 x y) (/.f64 z y))

series30.0ms (0.6%)

Counts

2 → 54

Calls

2 calls:

17.0ms	(fma.f64 4 (-.f64 (/.f64 x y) (/.f64 z y)) 2)
12.0ms	(-.f64 (/.f64 x y) (/.f64 z y))

rewrite83.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Rules

262×	`times-frac_binary64`
212×	`add-sqr-sqrt_binary64`
208×	`*-un-lft-identity_binary64`
200×	`add-cube-cbrt_binary64`
169×	`prod-diff_binary64`

Counts

2 → 229

Calls

2 calls:

19.0ms	(-.f64 (/.f64 x y) (/.f64 z y))
0.0ms	(fma.f64 4 (-.f64 (/.f64 x y) (/.f64 z y)) 2)

simplify204.0ms (4.3%)

Algorithm

1×	egg-herbie

Rules

524×	`associate-*l/_binary64`
471×	`associate-*r/_binary64`
386×	`associate-/l*_binary64`
310×	`fma-neg_binary64`
172×	`cancel-sign-sub-inv_binary64`

Counts

283 → 273

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	336	5308
1	738	4368
2	1479	2886
3	4239	2886
4	4798	2886
5	4793	2886

prune173.0ms (3.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	272	1	273
Fresh	1	1	2
Picked	0	1	1
Done	0	0	0
Total	273	3	276

Error

Counts

276 → 3

Alt Table

Status	Error	Program
	0.3b	(fma.f64 4 (+.f64 (/.f64 x y) (.f64 (neg.f64 (.f64 (cbrt.f64 (/.f64 z y)) (cbrt.f64 (/.f64 z y)))) (cbrt.f64 (/.f64 z y)))) 2)
✓	0.0b	(fma.f64 4 (-.f64 (/.f64 x y) (/.f64 z y)) 2)
▶	0.0b	(+.f64 1 (/.f64 (.f64 4 (-.f64 (+.f64 x (.f64 y 1/4)) z)) y))

Compiler

Compiled 9897 to 2674 computations (73% saved)

localize8.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 1 (/.f64 (.f64 4 (-.f64 (+.f64 x (.f64 y 1/4)) z)) y))
✓	0.0b	(/.f64 (.f64 4 (-.f64 (+.f64 x (.f64 y 1/4)) z)) y)

series35.0ms (0.7%)

Counts

2 → 72

Calls

2 calls:

18.0ms	(+.f64 1 (/.f64 (.f64 4 (-.f64 (+.f64 x (.f64 y 1/4)) z)) y))
17.0ms	(/.f64 (.f64 4 (-.f64 (+.f64 x (.f64 y 1/4)) z)) y)

rewrite16.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`*-un-lft-identity_binary64`
7×	`add-cbrt-cube_binary64`
7×	`add-exp-log_binary64`
5×	`add-sqr-sqrt_binary64`
5×	`add-cube-cbrt_binary64`

Counts

2 → 42

Calls

2 calls:

8.0ms	(/.f64 (.f64 4 (-.f64 (+.f64 x (.f64 y 1/4)) z)) y)
6.0ms	(+.f64 1 (/.f64 (.f64 4 (-.f64 (+.f64 x (.f64 y 1/4)) z)) y))

simplify75.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

510×	`div-sub_binary64`
373×	`distribute-rgt-in_binary64`
359×	`distribute-lft-in_binary64`
336×	`associate-/l*_binary64`
327×	`times-frac_binary64`

Counts

114 → 90

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	118	1603
1	306	1563
2	887	1346
3	4459	1342
4	5956	1342

prune67.0ms (1.4%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	90	0	90
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	90	3	93

Error

Counts

93 → 3

Alt Table

Status	Error	Program
▶	0.3b	(fma.f64 4 (+.f64 (/.f64 x y) (.f64 (neg.f64 (.f64 (cbrt.f64 (/.f64 z y)) (cbrt.f64 (/.f64 z y)))) (cbrt.f64 (/.f64 z y)))) 2)
✓	0.0b	(fma.f64 4 (-.f64 (/.f64 x y) (/.f64 z y)) 2)
✓	0.0b	(+.f64 1 (/.f64 (.f64 4 (-.f64 (+.f64 x (.f64 y 1/4)) z)) y))

Compiler

Compiled 1675 to 1083 computations (35.3% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (/.f64 x y) (.f64 (neg.f64 (.f64 (cbrt.f64 (/.f64 z y)) (cbrt.f64 (/.f64 z y)))) (cbrt.f64 (/.f64 z y))))
✓	0.3b	(.f64 (neg.f64 (.f64 (cbrt.f64 (/.f64 z y)) (cbrt.f64 (/.f64 z y)))) (cbrt.f64 (/.f64 z y)))
✓	0.5b	(*.f64 (cbrt.f64 (/.f64 z y)) (cbrt.f64 (/.f64 z y)))
✓	9.2b	(cbrt.f64 (/.f64 z y))

series1.2s (25.3%)

Counts

4 → 108

Calls

4 calls:

730.0ms	(*.f64 (cbrt.f64 (/.f64 z y)) (cbrt.f64 (/.f64 z y)))
404.0ms	(cbrt.f64 (/.f64 z y))
39.0ms	(.f64 (neg.f64 (.f64 (cbrt.f64 (/.f64 z y)) (cbrt.f64 (/.f64 z y)))) (cbrt.f64 (/.f64 z y)))
38.0ms	(+.f64 (/.f64 x y) (.f64 (neg.f64 (.f64 (cbrt.f64 (/.f64 z y)) (cbrt.f64 (/.f64 z y)))) (cbrt.f64 (/.f64 z y))))

rewrite44.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

92×	`cbrt-prod_binary64`
90×	`add-sqr-sqrt_binary64`
70×	`times-frac_binary64`
59×	`*-un-lft-identity_binary64`
59×	`add-cube-cbrt_binary64`

Counts

4 → 184

Calls

4 calls:

10.0ms	(*.f64 (cbrt.f64 (/.f64 z y)) (cbrt.f64 (/.f64 z y)))
9.0ms	(+.f64 (/.f64 x y) (.f64 (neg.f64 (.f64 (cbrt.f64 (/.f64 z y)) (cbrt.f64 (/.f64 z y)))) (cbrt.f64 (/.f64 z y))))
8.0ms	(.f64 (neg.f64 (.f64 (cbrt.f64 (/.f64 z y)) (cbrt.f64 (/.f64 z y)))) (cbrt.f64 (/.f64 z y)))
2.0ms	(cbrt.f64 (/.f64 z y))

simplify171.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

420×	`fma-def_binary64`
419×	`fma-neg_binary64`
387×	`times-frac_binary64`
291×	`associate-l_binary64`
283×	`associate-r_binary64`

Counts

292 → 283

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	288	4759
1	636	4568
2	2051	4236
3	4597	4236
4	5108	4236

prune242.0ms (5.1%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	355	0	355
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	355	3	358

Error

Counts

358 → 3

Alt Table

Status	Error	Program
✓	0.3b	(fma.f64 4 (+.f64 (/.f64 x y) (.f64 (neg.f64 (.f64 (cbrt.f64 (/.f64 z y)) (cbrt.f64 (/.f64 z y)))) (cbrt.f64 (/.f64 z y)))) 2)
✓	0.0b	(fma.f64 4 (-.f64 (/.f64 x y) (/.f64 z y)) 2)
✓	0.0b	(+.f64 1 (/.f64 (.f64 4 (-.f64 (+.f64 x (.f64 y 1/4)) z)) y))

Compiler

Compiled 10237 to 3151 computations (69.2% saved)

regimes252.0ms (5.3%)

Accuracy

Total 0.0b remaining (69.5%)

Threshold costs 0.0b (69.5%)

Counts

54 → 1

Compiler

Compiled 3701 to 2685 computations (27.5% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	14
1	12	14
2	19	14
3	23	14
4	26	14
5	27	14
6	27	14

end59.0ms (1.2%)

Compiler: Compiled 80 to 52 computations (35% saved)

Details

analyze514.0ms (10.7%)

sample1.2s (24.2%)

simplify62.0ms (1.3%)

prune4.0ms (0.1%)

localize5.0ms (0.1%)

series28.0ms (0.6%)

rewrite7.0ms (0.2%)

simplify170.0ms (3.5%)

prune150.0ms (3.1%)

localize6.0ms (0.1%)

series30.0ms (0.6%)

rewrite83.0ms (1.7%)

simplify204.0ms (4.3%)

prune173.0ms (3.6%)

localize8.0ms (0.2%)

series35.0ms (0.7%)

rewrite16.0ms (0.3%)

simplify75.0ms (1.6%)

prune67.0ms (1.4%)

localize13.0ms (0.3%)

series1.2s (25.3%)

rewrite44.0ms (0.9%)

simplify171.0ms (3.6%)

prune242.0ms (5.1%)

regimes252.0ms (5.3%)

simplify3.0ms (0.1%)

end59.0ms (1.2%)

Profiling