Details

analyze122.0ms (4.6%)

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
25%	74.9%	0.1%	4
43.7%	56.2%	0.1%	5
65.6%	34.3%	0.1%	6
76.5%	23.4%	0.1%	7
82%	18%	0.1%	8
87.8%	12.1%	0.1%	9
90.7%	9.2%	0.1%	10
93.8%	6.1%	0.1%	11
95.3%	4.6%	0.1%	12
96.8%	3.1%	0.1%	13
97.6%	2.3%	0.1%	14

Compiler

Compiled 8 to 5 computations (37.5% saved)

sample26.0ms (1%)

Algorithm

1×

intervals

Results

12.0ms

256×

body

128

valid

Compiler

Compiled 17 to 11 computations (35.3% saved)

simplify13.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	7
1	6	7
2	6	7

prune3.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

0.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.0b	(/.f64 x (+.f64 y x))

Compiler

Compiled 26 to 14 computations (46.2% saved)

localize6.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 x (+.f64 y x))

series19.0ms (0.7%)

Counts

1 → 24

Calls

1 calls:

19.0ms

(/.f64 x (+.f64 y x))

rewrite11.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`*-un-lft-identity_binary64`
12×	`times-frac_binary64`
10×	`add-sqr-sqrt_binary64`
10×	`add-cube-cbrt_binary64`
4×	`associate-/r*_binary64`

Counts

1 → 35

Calls

1 calls:

7.0ms

(/.f64 x (+.f64 y x))

simplify81.0ms (3%)

Algorithm

1×	egg-herbie

Rules

614×	`fma-def_binary64`
547×	`associate-/r*_binary64`
430×	`associate-/l/_binary64`
325×	`associate-/r/_binary64`
276×	`cancel-sign-sub-inv_binary64`

Counts

59 → 68

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	84	914
1	184	884
2	477	833
3	1577	791
4	4946	791

prune74.0ms (2.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	64	4	68
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	64	5	69

Error

Counts

69 → 5

Alt Table

Status	Error	Program
	32.4b	(fma.f64 (/.f64 y x) (+.f64 (/.f64 y x) -1) 1)
✓	0.0b	(/.f64 x (+.f64 y x))
	1.3b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (cbrt.f64 x) (+.f64 x y)))
▶	0.6b	(.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (cbrt.f64 (+.f64 y x)) (cbrt.f64 (+.f64 y x)))) (/.f64 (cbrt.f64 x) (cbrt.f64 (+.f64 y x))))
	12.2b	(cbrt.f64 (.f64 (.f64 (/.f64 x (+.f64 y x)) (/.f64 x (+.f64 y x))) (/.f64 x (+.f64 y x))))

Compiler

Compiled 991 to 328 computations (66.9% saved)

localize21.0ms (0.8%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
✓	0.5b	(*.f64 (cbrt.f64 (+.f64 y x)) (cbrt.f64 (+.f64 y x)))
✓	0.6b	(cbrt.f64 (+.f64 y x))
✓	0.6b	(cbrt.f64 x)

series233.0ms (8.7%)

Counts

4 → 72

Calls

4 calls:

73.0ms	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
72.0ms	(cbrt.f64 x)
46.0ms	(*.f64 (cbrt.f64 (+.f64 y x)) (cbrt.f64 (+.f64 y x)))
41.0ms	(cbrt.f64 (+.f64 y x))

rewrite52.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Rules

47×	`cbrt-prod_binary64`
38×	`*-un-lft-identity_binary64`
38×	`add-sqr-sqrt_binary64`
22×	`add-cube-cbrt_binary64`
18×	`pow1_binary64`

Counts

4 → 126

Calls

4 calls:

17.0ms	(*.f64 (cbrt.f64 (+.f64 y x)) (cbrt.f64 (+.f64 y x)))
9.0ms	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
7.0ms	(cbrt.f64 (+.f64 y x))
1.0ms	(cbrt.f64 x)

simplify238.0ms (8.9%)

Algorithm

1×	egg-herbie

Rules

713×	`fma-def_binary64`
464×	`unswap-sqr_binary64`
345×	`fma-neg_binary64`
300×	`cancel-sign-sub-inv_binary64`
237×	`associate-r_binary64`

Counts

198 → 219

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	245	3549
1	597	3359
2	2059	3012
3	4029	2873
4	4817	2873
5	5035	2873

prune411.0ms (15.3%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	363	0	363
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	363	5	368

Error

Counts

368 → 5

Alt Table

Status	Error	Program
	32.4b	(fma.f64 (/.f64 y x) (+.f64 (/.f64 y x) -1) 1)
✓	0.0b	(/.f64 x (+.f64 y x))
▶	1.3b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (cbrt.f64 x) (+.f64 x y)))
✓	0.6b	(.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (cbrt.f64 (+.f64 y x)) (cbrt.f64 (+.f64 y x)))) (/.f64 (cbrt.f64 x) (cbrt.f64 (+.f64 y x))))
	12.2b	(cbrt.f64 (.f64 (.f64 (/.f64 x (+.f64 y x)) (/.f64 x (+.f64 y x))) (/.f64 x (+.f64 y x))))

Compiler

Compiled 12162 to 3442 computations (71.7% saved)

localize14.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (cbrt.f64 x) (+.f64 x y)))
✓	0.3b	(/.f64 (cbrt.f64 x) (+.f64 x y))
	0.5b	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
	0.6b	(cbrt.f64 x)

series79.0ms (2.9%)

Counts

2 → 48

Calls

2 calls:

57.0ms	(/.f64 (cbrt.f64 x) (+.f64 x y))
21.0ms	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (cbrt.f64 x) (+.f64 x y)))

rewrite54.0ms (2%)

Algorithm

1×	rewrite-expression-head

Rules

60×	`*-un-lft-identity_binary64`
50×	`times-frac_binary64`
39×	`add-sqr-sqrt_binary64`
34×	`add-cube-cbrt_binary64`
30×	`associate-r_binary64`

Counts

2 → 105

Calls

2 calls:

27.0ms	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (cbrt.f64 x) (+.f64 x y)))
9.0ms	(/.f64 (cbrt.f64 x) (+.f64 x y))

simplify194.0ms (7.2%)

Algorithm

1×	egg-herbie

Rules

926×	`times-frac_binary64`
410×	`fma-def_binary64`
407×	`fma-neg_binary64`
305×	`cancel-sign-sub-inv_binary64`
223×	`associate-l_binary64`

Counts

153 → 193

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	210	3097
1	554	2748
2	2061	2680
3	4520	2671
4	4994	2671
5	4932	2671

prune126.0ms (4.7%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	303	1	304
Fresh	1	1	2
Picked	0	1	1
Done	0	2	2
Total	304	5	309

Error

Counts

309 → 5

Alt Table

Status	Error	Program
	32.4b	(fma.f64 (/.f64 y x) (+.f64 (/.f64 y x) -1) 1)
✓	0.0b	(/.f64 x (+.f64 y x))
▶	12.2b	(cbrt.f64 (pow.f64 (/.f64 x (+.f64 y x)) 3))
✓	1.3b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (cbrt.f64 x) (+.f64 x y)))
✓	0.6b	(.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (cbrt.f64 (+.f64 y x)) (cbrt.f64 (+.f64 y x)))) (/.f64 (cbrt.f64 x) (cbrt.f64 (+.f64 y x))))

Compiler

Compiled 5919 to 1613 computations (72.7% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(/.f64 x (+.f64 y x))
✓	0.1b	(pow.f64 (/.f64 x (+.f64 y x)) 3)
✓	12.2b	(cbrt.f64 (pow.f64 (/.f64 x (+.f64 y x)) 3))

series32.0ms (1.2%)

Counts

2 → 48

Calls

2 calls:

18.0ms	(pow.f64 (/.f64 x (+.f64 y x)) 3)
14.0ms	(cbrt.f64 (pow.f64 (/.f64 x (+.f64 y x)) 3))

rewrite20.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

60×	`*-un-lft-identity_binary64`
48×	`times-frac_binary64`
42×	`cbrt-prod_binary64`
36×	`cube-prod_binary64`
36×	`add-sqr-sqrt_binary64`

Counts

2 → 112

Calls

2 calls:

5.0ms	(cbrt.f64 (pow.f64 (/.f64 x (+.f64 y x)) 3))
5.0ms	(pow.f64 (/.f64 x (+.f64 y x)) 3)

simplify81.0ms (3%)

Algorithm

1×	egg-herbie

Rules

732×	`associate-/l*_binary64`
333×	`unswap-sqr_binary64`
281×	`fma-def_binary64`
276×	`associate-/r/_binary64`
265×	`associate-/l/_binary64`

Counts

160 → 147

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	197	3000
1	520	2807
2	1608	2655
3	5271	2655

prune140.0ms (5.2%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	214	1	215
Fresh	1	0	1
Picked	0	1	1
Done	0	3	3
Total	215	5	220

Error

Counts

220 → 5

Alt Table

Status	Error	Program
✓	0.0b	(/.f64 x (+.f64 y x))
	17.7b	(cbrt.f64 (*.f64 (pow.f64 (sqrt.f64 (/.f64 x (+.f64 y x))) 3) (pow.f64 (sqrt.f64 (/.f64 x (+.f64 y x))) 3)))
✓	12.2b	(cbrt.f64 (pow.f64 (/.f64 x (+.f64 y x)) 3))
✓	1.3b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (cbrt.f64 x) (+.f64 x y)))
✓	0.6b	(.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (cbrt.f64 (+.f64 y x)) (cbrt.f64 (+.f64 y x)))) (/.f64 (cbrt.f64 x) (cbrt.f64 (+.f64 y x))))

Compiler

Compiled 3417 to 1511 computations (55.8% saved)

regimes165.0ms (6.1%)

Accuracy

Total 0.0b remaining (54.2%)

Threshold costs 0.0b (54.2%)

Counts

62 → 1

Compiler

Compiled 3125 to 1744 computations (44.2% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	7
1	6	7
2	6	7

end0.0ms (0%)

Compiler: Compiled 7 to 4 computations (42.9% saved)

sample465.0ms (17.3%)

Algorithm

1×

intervals

Results

200.0ms

8000×

body

128

valid

Compiler

Compiled 93 to 50 computations (46.2% saved)

Details

analyze122.0ms (4.6%)

sample26.0ms (1%)

simplify13.0ms (0.5%)

prune3.0ms (0.1%)

localize6.0ms (0.2%)

series19.0ms (0.7%)

rewrite11.0ms (0.4%)

simplify81.0ms (3%)

prune74.0ms (2.8%)

localize21.0ms (0.8%)

series233.0ms (8.7%)

rewrite52.0ms (1.9%)

simplify238.0ms (8.9%)

prune411.0ms (15.3%)

localize14.0ms (0.5%)

series79.0ms (2.9%)

rewrite54.0ms (2%)

simplify194.0ms (7.2%)

prune126.0ms (4.7%)

localize6.0ms (0.2%)

series32.0ms (1.2%)

rewrite20.0ms (0.8%)

simplify81.0ms (3%)

prune140.0ms (5.2%)

regimes165.0ms (6.1%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample465.0ms (17.3%)

Profiling