Details

analyze478.0ms (14.9%)

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
0%	99.9%	0.1%	7
0%	99.9%	0.1%	8
0%	99.9%	0.1%	9
46%	49.5%	4.4%	10
50.3%	44.9%	4.8%	11
55.6%	39.2%	5.2%	12
62.9%	25.7%	11.4%	13
65.2%	23.2%	11.7%	14

Compiler

Compiled 15 to 11 computations (26.7% saved)

sample101.0ms (3.2%)

Algorithm

1×

intervals

Results

12.0ms	256×	body	128	valid
1.0ms	29×	body	128	invalid

Compiler

Compiled 32 to 24 computations (25% saved)

simplify109.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

925×	`fma-neg_binary64`
880×	`div-sub_binary64`
795×	`fma-def_binary64`
774×	`times-frac_binary64`
463×	`cancel-sign-sub-inv_binary64`

Counts

1 → 2

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	11	16
1	24	16
2	57	14
3	172	14
4	408	14
5	1241	11
6	2694	11
7	4033	11
8	4216	11
9	4586	11
10	4475	11
11	4492	11
12	4700	11

prune3.0ms (0.1%)

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 4 (/.f64 (-.f64 x y) z) -2)

Compiler

Compiled 44 to 30 computations (31.8% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

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

series23.0ms (0.7%)

Counts

2 → 64

Calls

2 calls:

12.0ms	(fma.f64 4 (/.f64 (-.f64 x y) z) -2)
11.0ms	(/.f64 (-.f64 x y) z)

rewrite12.0ms (0.4%)

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:

9.0ms	(/.f64 (-.f64 x y) z)
0.0ms	(fma.f64 4 (/.f64 (-.f64 x y) z) -2)

simplify78.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

539×	`times-frac_binary64`
464×	`distribute-rgt-in_binary64`
455×	`distribute-lft-in_binary64`
431×	`associate-/l*_binary64`
329×	`fma-def_binary64`

Counts

114 → 78

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	107	1444
1	240	1279
2	508	1223
3	1185	1223
4	4371	1223
5	5014	1223

prune45.0ms (1.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	76	2	78
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	76	3	79

Error

Counts

79 → 3

Alt Table

Status	Error	Program
✓	0.0b	(fma.f64 4 (/.f64 (-.f64 x y) z) -2)
▶	0.8b	(fma.f64 4 (/.f64 (*.f64 (cbrt.f64 (-.f64 x y)) (cbrt.f64 (-.f64 x y))) (/.f64 z (cbrt.f64 (-.f64 x y)))) -2)
	18.4b	(fma.f64 x (/.f64 4 z) -2)

Compiler

Compiled 1106 to 504 computations (54.4% saved)

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 z (cbrt.f64 (-.f64 x y)))
✓	0.3b	(/.f64 (*.f64 (cbrt.f64 (-.f64 x y)) (cbrt.f64 (-.f64 x y))) (/.f64 z (cbrt.f64 (-.f64 x y))))
✓	0.5b	(*.f64 (cbrt.f64 (-.f64 x y)) (cbrt.f64 (-.f64 x y)))
✓	0.6b	(cbrt.f64 (-.f64 x y))

series419.0ms (13.1%)

Counts

4 → 120

Calls

4 calls:

329.0ms	(/.f64 z (cbrt.f64 (-.f64 x y)))
39.0ms	(*.f64 (cbrt.f64 (-.f64 x y)) (cbrt.f64 (-.f64 x y)))
30.0ms	(cbrt.f64 (-.f64 x y))
20.0ms	(/.f64 (*.f64 (cbrt.f64 (-.f64 x y)) (cbrt.f64 (-.f64 x y))) (/.f64 z (cbrt.f64 (-.f64 x y))))

rewrite53.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Rules

102×	`times-frac_binary64`
98×	`add-sqr-sqrt_binary64`
96×	`*-un-lft-identity_binary64`
83×	`cbrt-prod_binary64`
60×	`add-cube-cbrt_binary64`

Counts

4 → 216

Calls

4 calls:

16.0ms	(/.f64 (*.f64 (cbrt.f64 (-.f64 x y)) (cbrt.f64 (-.f64 x y))) (/.f64 z (cbrt.f64 (-.f64 x y))))
10.0ms	(*.f64 (cbrt.f64 (-.f64 x y)) (cbrt.f64 (-.f64 x y)))
4.0ms	(/.f64 z (cbrt.f64 (-.f64 x y)))
2.0ms	(cbrt.f64 (-.f64 x y))

simplify590.0ms (18.5%)

Algorithm

1×	egg-herbie

Rules

368×	`associate-r_binary64`
316×	`associate-/l*_binary64`
293×	`associate-l_binary64`
269×	`*-commutative_binary64`
200×	`fma-def_binary64`

Counts

336 → 387

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	489	8415
1	1264	7648
2	4657	7322
3	4976	7322

prune378.0ms (11.8%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	491	0	491
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	491	3	494

Error

Counts

494 → 3

Alt Table

Status	Error	Program
✓	0.0b	(fma.f64 4 (/.f64 (-.f64 x y) z) -2)
✓	0.8b	(fma.f64 4 (/.f64 (*.f64 (cbrt.f64 (-.f64 x y)) (cbrt.f64 (-.f64 x y))) (/.f64 z (cbrt.f64 (-.f64 x y)))) -2)
▶	18.4b	(fma.f64 x (/.f64 4 z) -2)

Compiler

Compiled 15643 to 6362 computations (59.3% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 x (/.f64 4 z) -2)

series5.0ms (0.2%)

Counts

1 → 24

Calls

1 calls:

5.0ms

(fma.f64 x (/.f64 4 z) -2)

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

1 → 10

Calls

1 calls:

0.0ms

(fma.f64 x (/.f64 4 z) -2)

simplify58.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

715×	`distribute-rgt-in_binary64`
695×	`distribute-lft-in_binary64`
524×	`associate-/l*_binary64`
452×	`distribute-rgt-out_binary64`
413×	`fma-def_binary64`

Counts

34 → 22

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	21	295
1	32	278
2	54	278
3	149	278
4	505	278
5	1786	278
6	4929	278
7	5117	278

prune13.0ms (0.4%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	22	0	22
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	22	3	25

Error

Counts

25 → 3

Alt Table

Status	Error	Program
✓	0.0b	(fma.f64 4 (/.f64 (-.f64 x y) z) -2)
✓	0.8b	(fma.f64 4 (/.f64 (*.f64 (cbrt.f64 (-.f64 x y)) (cbrt.f64 (-.f64 x y))) (/.f64 z (cbrt.f64 (-.f64 x y)))) -2)
✓	18.4b	(fma.f64 x (/.f64 4 z) -2)

Compiler

Compiled 264 to 177 computations (33% saved)

regimes103.0ms (3.2%)

Accuracy

Total 0.0b remaining (28.6%)

Threshold costs 0.0b (28.6%)

Counts

19 → 1

Compiler

Compiled 1215 to 865 computations (28.8% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	11
1	11	11
2	16	11
3	18	11
4	19	11
5	19	11

end0.0ms (0%)

Compiler: Compiled 11 to 8 computations (27.3% saved)

sample708.0ms (22.2%)

Algorithm

1×

intervals

Results

358.0ms	8000×	body	128	valid
37.0ms	934×	body	128	invalid

Compiler

Compiled 71 to 48 computations (32.4% saved)

Details

analyze478.0ms (14.9%)

sample101.0ms (3.2%)

simplify109.0ms (3.4%)

prune3.0ms (0.1%)

localize5.0ms (0.2%)

series23.0ms (0.7%)

rewrite12.0ms (0.4%)

simplify78.0ms (2.4%)

prune45.0ms (1.4%)

localize9.0ms (0.3%)

series419.0ms (13.1%)

rewrite53.0ms (1.7%)

simplify590.0ms (18.5%)

prune378.0ms (11.8%)

localize4.0ms (0.1%)

series5.0ms (0.2%)

rewrite1.0ms (0%)

simplify58.0ms (1.8%)

prune13.0ms (0.4%)

regimes103.0ms (3.2%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample708.0ms (22.2%)

Profiling