Details

analyze139.0ms (3.7%)

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
25%	74.9%	0.1%	5
37.5%	50%	12.6%	6
50%	37.5%	12.6%	7
56.2%	25%	18.8%	8
62.4%	18.7%	18.8%	9
65.6%	12.5%	22%	10
68.7%	9.4%	22%	11
70.2%	6.2%	23.5%	12
71.8%	4.7%	23.5%	13
72.6%	3.1%	24.3%	14

Compiler

Compiled 10 to 7 computations (30% saved)

sample17.0ms (0.5%)

Algorithm

1×

intervals

Results

8.0ms	256×	body	128	valid
0.0ms	2×	body	128	invalid

Compiler

Compiled 21 to 15 computations (28.6% saved)

simplify33.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

265×	`fma-def_binary64`
84×	`fma-neg_binary64`
35×	`distribute-rgt-in_binary64`
26×	`unsub-neg_binary64`
25×	`sub-neg_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	16	10
2	31	10
3	63	10
4	134	10
5	183	10
6	236	10
7	328	10
8	360	10
9	359	10
10	389	10
11	346	10

prune3.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

0.1b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.1b	(.f64 x (-.f64 1 (.f64 x y)))

Compiler

Compiled 27 to 18 computations (33.3% saved)

localize8.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 x (-.f64 1 (.f64 x y)))

series10.0ms (0.3%)

Counts

1 → 24

Calls

1 calls:

10.0ms

(*.f64 x (-.f64 1 (*.f64 x y)))

rewrite8.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`add-sqr-sqrt_binary64`
6×	`prod-diff_binary64`
5×	`distribute-lft-in_binary64`
5×	`distribute-rgt-in_binary64`
5×	`*-un-lft-identity_binary64`

Counts

1 → 32

Calls

1 calls:

5.0ms

(*.f64 x (-.f64 1 (*.f64 x y)))

simplify78.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

888×	`fma-def_binary64`
584×	`unsub-neg_binary64`
561×	`distribute-neg-out_binary64`
311×	`associate-l_binary64`
293×	`unswap-sqr_binary64`

Counts

56 → 51

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	69	723
1	140	663
2	421	626
3	1318	606
4	2818	606
5	5568	606

prune75.0ms (2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	44	7	51
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	44	8	52

Error

Counts

52 → 8

Alt Table

Status	Error	Program
	1.4b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (cbrt.f64 x) (-.f64 1 (.f64 x y))))
	22.4b	(/.f64 (fma.f64 (pow.f64 x 3) (.f64 y (neg.f64 y)) x) (+.f64 1 (.f64 x y)))
	8.4b	(/.f64 (.f64 x (-.f64 (.f64 1 1) (.f64 (.f64 x y) (.f64 x y)))) (+.f64 1 (.f64 x y)))
✓	0.1b	(.f64 x (-.f64 1 (.f64 x y)))
	28.7b	(.f64 (sqrt.f64 (.f64 x (-.f64 1 (.f64 x y)))) (sqrt.f64 (.f64 x (-.f64 1 (*.f64 x y)))))
	44.9b	(cbrt.f64 (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 (-.f64 1 (.f64 x y)) (-.f64 1 (.f64 x y))) (-.f64 1 (.f64 x y)))))
▶	1.3b	(.f64 (.f64 (cbrt.f64 (.f64 x (-.f64 1 (.f64 x y)))) (cbrt.f64 (.f64 x (-.f64 1 (.f64 x y))))) (cbrt.f64 (.f64 x (-.f64 1 (.f64 x y)))))
	7.8b	(-.f64 x (*.f64 y (pow.f64 x 2)))

Compiler

Compiled 977 to 463 computations (52.6% saved)

localize17.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(.f64 x (-.f64 1 (.f64 x y)))
✓	0.3b	(.f64 (.f64 (cbrt.f64 (.f64 x (-.f64 1 (.f64 x y)))) (cbrt.f64 (.f64 x (-.f64 1 (.f64 x y))))) (cbrt.f64 (.f64 x (-.f64 1 (.f64 x y)))))
✓	0.4b	(.f64 (cbrt.f64 (.f64 x (-.f64 1 (.f64 x y)))) (cbrt.f64 (.f64 x (-.f64 1 (*.f64 x y)))))
✓	0.6b	(cbrt.f64 (.f64 x (-.f64 1 (.f64 x y))))

series121.0ms (3.2%)

Counts

3 → 72

Calls

3 calls:

56.0ms

(*.f64 (cbrt.f64 (*.f64 x (-.f64 1 (*.f64 x y)))) (cbrt.f64 (*.f64 x (-.f64 1 (*.f64 x y)))))

37.0ms

(cbrt.f64 (*.f64 x (-.f64 1 (*.f64 x y))))

28.0ms

(*.f64 (*.f64 (cbrt.f64 (*.f64 x (-.f64 1 (*.f64 x y)))) (cbrt.f64 (*.f64 x (-.f64 1 (*.f64 x y))))) (cbrt.f64 (*.f64 x (-.f64 1 (*.f64 x y)))))

rewrite72.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Rules

78×	`associate-*r/_binary64`
68×	`cbrt-div_binary64`
34×	`flip--_binary64`
34×	`flip3--_binary64`
32×	`frac-times_binary64`

Counts

3 → 115

Calls

3 calls:

18.0ms

(*.f64 (*.f64 (cbrt.f64 (*.f64 x (-.f64 1 (*.f64 x y)))) (cbrt.f64 (*.f64 x (-.f64 1 (*.f64 x y))))) (cbrt.f64 (*.f64 x (-.f64 1 (*.f64 x y)))))

12.0ms

(*.f64 (cbrt.f64 (*.f64 x (-.f64 1 (*.f64 x y)))) (cbrt.f64 (*.f64 x (-.f64 1 (*.f64 x y)))))

6.0ms

(cbrt.f64 (*.f64 x (-.f64 1 (*.f64 x y))))

simplify280.0ms (7.4%)

Algorithm

1×	egg-herbie

Rules

734×	`cancel-sign-sub-inv_binary64`
304×	`associate-/r*_binary64`
208×	`associate-l_binary64`
192×	`sub-neg_binary64`
192×	`times-frac_binary64`

Counts

187 → 247

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	330	6638
1	922	6109
2	3303	5782
3	5086	5782

prune850.0ms (22.5%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	522	2	524
Fresh	2	4	6
Picked	0	1	1
Done	0	1	1
Total	524	8	532

Error

Counts

532 → 8

Alt Table

Status	Error	Program
	1.4b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (cbrt.f64 x) (-.f64 1 (.f64 x y))))
	22.4b	(/.f64 (fma.f64 (pow.f64 x 3) (.f64 y (neg.f64 y)) x) (+.f64 1 (.f64 x y)))
	42.1b	(cbrt.f64 (pow.f64 (-.f64 x (.f64 x (.f64 x y))) 3))
✓	0.1b	(.f64 x (-.f64 1 (.f64 x y)))
	28.7b	(.f64 (sqrt.f64 (.f64 x (-.f64 1 (.f64 x y)))) (sqrt.f64 (.f64 x (-.f64 1 (*.f64 x y)))))
✓	1.3b	(.f64 (.f64 (cbrt.f64 (.f64 x (-.f64 1 (.f64 x y)))) (cbrt.f64 (.f64 x (-.f64 1 (.f64 x y))))) (cbrt.f64 (.f64 x (-.f64 1 (.f64 x y)))))
▶	0.1b	(-.f64 x (.f64 x (.f64 x y)))
	7.8b	(-.f64 x (*.f64 y (pow.f64 x 2)))

Compiler

Compiled 21628 to 11954 computations (44.7% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 x (.f64 x (.f64 x y)))
✓	0.2b	(.f64 x (.f64 x y))

series27.0ms (0.7%)

Counts

2 → 48

Calls

2 calls:

15.0ms	(.f64 x (.f64 x y))
12.0ms	(-.f64 x (.f64 x (.f64 x y)))

rewrite13.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`add-cbrt-cube_binary64`
7×	`add-exp-log_binary64`
7×	`pow1_binary64`
5×	`*-un-lft-identity_binary64`
5×	`add-sqr-sqrt_binary64`

Counts

2 → 40

Calls

2 calls:

6.0ms	(.f64 x (.f64 x y))
4.0ms	(-.f64 x (.f64 x (.f64 x y)))

simplify128.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

598×	`fma-def_binary64`
391×	`fma-neg_binary64`
321×	`times-frac_binary64`
278×	`distribute-rgt-neg-in_binary64`
265×	`distribute-lft-neg-in_binary64`

Counts

88 → 69

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	72	910
1	172	861
2	507	831
3	1316	829
4	3540	829
5	4548	829
6	4792	829

prune76.0ms (2%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	68	1	69
Fresh	1	4	5
Picked	0	1	1
Done	0	2	2
Total	69	8	77

Error

Counts

77 → 8

Alt Table

Status	Error	Program
	8.0b	(-.f64 x (.f64 (.f64 (cbrt.f64 (.f64 y (.f64 x x))) (cbrt.f64 (.f64 y (.f64 x x)))) (cbrt.f64 (.f64 y (.f64 x x)))))
	7.8b	(-.f64 x (*.f64 y (pow.f64 x 2)))
▶	1.4b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (cbrt.f64 x) (-.f64 1 (.f64 x y))))
	22.4b	(/.f64 (fma.f64 (pow.f64 x 3) (.f64 y (neg.f64 y)) x) (+.f64 1 (.f64 x y)))
✓	0.1b	(.f64 x (-.f64 1 (.f64 x y)))
	28.7b	(.f64 (sqrt.f64 (.f64 x (-.f64 1 (.f64 x y)))) (sqrt.f64 (.f64 x (-.f64 1 (*.f64 x y)))))
✓	1.3b	(.f64 (.f64 (cbrt.f64 (.f64 x (-.f64 1 (.f64 x y)))) (cbrt.f64 (.f64 x (-.f64 1 (.f64 x y))))) (cbrt.f64 (.f64 x (-.f64 1 (.f64 x y)))))
✓	0.1b	(-.f64 x (.f64 x (.f64 x y)))

Compiler

Compiled 1088 to 337 computations (69% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (cbrt.f64 x) (-.f64 1 (.f64 x y)))
✓	0.3b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (cbrt.f64 x) (-.f64 1 (.f64 x y))))
✓	0.5b	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
✓	0.6b	(cbrt.f64 x)

series271.0ms (7.2%)

Counts

4 → 72

Calls

4 calls:

121.0ms	(.f64 (cbrt.f64 x) (-.f64 1 (.f64 x y)))
64.0ms	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
61.0ms	(cbrt.f64 x)
24.0ms	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (cbrt.f64 x) (-.f64 1 (.f64 x y))))

rewrite51.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

34×	`add-sqr-sqrt_binary64`
25×	`distribute-lft-in_binary64`
25×	`distribute-rgt-in_binary64`
25×	`pow1_binary64`
23×	`cbrt-prod_binary64`

Counts

4 → 137

Calls

4 calls:

13.0ms	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (cbrt.f64 x) (-.f64 1 (.f64 x y))))
11.0ms	(.f64 (cbrt.f64 x) (-.f64 1 (.f64 x y)))
9.0ms	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
1.0ms	(cbrt.f64 x)

simplify218.0ms (5.8%)

Algorithm

1×	egg-herbie

Rules

500×	`exp-prod_binary64`
419×	`fma-neg_binary64`
398×	`fma-def_binary64`
345×	`associate-l_binary64`
291×	`distribute-rgt-in_binary64`

Counts

209 → 195

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	168	2627
1	348	2339
2	1356	2193
3	3351	2063
4	4202	1965
5	4737	1965
6	4598	1965

prune167.0ms (4.4%)

Pruning

8 alts after pruning (4 fresh and 4 done)

	Pruned	Kept	Total
New	231	0	231
Fresh	0	4	4
Picked	0	1	1
Done	0	3	3
Total	231	8	239

Error

Counts

239 → 8

Alt Table

Status	Error	Program
	8.0b	(-.f64 x (.f64 (.f64 (cbrt.f64 (.f64 y (.f64 x x))) (cbrt.f64 (.f64 y (.f64 x x)))) (cbrt.f64 (.f64 y (.f64 x x)))))
	7.8b	(-.f64 x (*.f64 y (pow.f64 x 2)))
✓	1.4b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (cbrt.f64 x) (-.f64 1 (.f64 x y))))
	22.4b	(/.f64 (fma.f64 (pow.f64 x 3) (.f64 y (neg.f64 y)) x) (+.f64 1 (.f64 x y)))
✓	0.1b	(.f64 x (-.f64 1 (.f64 x y)))
	28.7b	(.f64 (sqrt.f64 (.f64 x (-.f64 1 (.f64 x y)))) (sqrt.f64 (.f64 x (-.f64 1 (*.f64 x y)))))
✓	1.3b	(.f64 (.f64 (cbrt.f64 (.f64 x (-.f64 1 (.f64 x y)))) (cbrt.f64 (.f64 x (-.f64 1 (.f64 x y))))) (cbrt.f64 (.f64 x (-.f64 1 (.f64 x y)))))
✓	0.1b	(-.f64 x (.f64 x (.f64 x y)))

Compiler

Compiled 4749 to 1712 computations (64% saved)

regimes201.0ms (5.3%)

Accuracy

Total 0.1b remaining (73.6%)

Threshold costs 0.1b (73.6%)

Counts

44 → 1

Compiler

Compiled 2604 to 1590 computations (38.9% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

7×	`*-commutative_binary64`
5×	`+-commutative_binary64`
5×	`distribute-rgt-neg-in_binary64`
4×	`distribute-lft-neg-in_binary64`
4×	`sub-neg_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	12
1	24	10
2	41	10
3	48	10
4	51	10
5	49	10

end1.0ms (0%)

Compiler: Compiled 9 to 5 computations (44.4% saved)

sample887.0ms (23.5%)

Algorithm

1×

intervals

Results

412.0ms	8000×	body	128	valid
5.0ms	79×	body	128	invalid

Compiler

Compiled 152 to 88 computations (42.1% saved)

Iter	Nodes	Cost
0	7	10
1	16	10
2	31	10
3	63	10
4	134	10
5	183	10
6	236	10
7	328	10
8	360	10
9	359	10
10	389	10
11	346	10

Iter	Nodes	Cost
0	7	10
1	16	10
2	31	10
3	63	10
4	134	10
5	183	10
6	236	10
7	328	10
8	360	10
9	359	10
10	389	10
11	346	10

Details

analyze139.0ms (3.7%)

sample17.0ms (0.5%)

simplify33.0ms (0.9%)

prune3.0ms (0.1%)

localize8.0ms (0.2%)

series10.0ms (0.3%)

rewrite8.0ms (0.2%)

simplify78.0ms (2.1%)

prune75.0ms (2%)

localize17.0ms (0.5%)

series121.0ms (3.2%)

rewrite72.0ms (1.9%)

simplify280.0ms (7.4%)

prune850.0ms (22.5%)

localize5.0ms (0.1%)

series27.0ms (0.7%)

rewrite13.0ms (0.4%)

simplify128.0ms (3.4%)

prune76.0ms (2%)

localize9.0ms (0.2%)

series271.0ms (7.2%)

rewrite51.0ms (1.4%)

simplify218.0ms (5.8%)

prune167.0ms (4.4%)

regimes201.0ms (5.3%)

simplify4.0ms (0.1%)

end1.0ms (0%)

sample887.0ms (23.5%)

Profiling

Iter	Nodes	Cost
0	7	10
1	16	10
2	31	10
3	63	10
4	134	10
5	183	10
6	236	10
7	328	10
8	360	10
9	359	10
10	389	10
11	346	10