Details

analyze79.0ms (4%)

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)

sample710.0ms (35.5%)

Results

656.0ms	8256×	body	128	valid
9.0ms	98×	body	128	invalid

Compiler

Compiled 29 to 20 computations (31% saved)

simplify17.0ms (0.8%)

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

prune1.0ms (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)

localize4.0ms (0.2%)

Local error

Found 1 expressions with local error:

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

series7.0ms (0.4%)

Counts

1 → 24

Calls

1 calls:

7.0ms

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

rewrite6.0ms (0.3%)

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:

4.0ms

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

simplify64.0ms (3.2%)

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

prune39.0ms (1.9%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	44	7	51
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	45	7	52

Error

0.0b

Counts

52 → 7

Alt Table

Status	Error	Program
	1.4b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (cbrt.f64 x) (-.f64 1 (.f64 x y))))
	10.3b	(-.f64 x (*.f64 y (pow.f64 x 2)))
▶	0.1b	(+.f64 (.f64 (fma.f64 1 1 (neg.f64 (.f64 y x))) x) (.f64 (fma.f64 (neg.f64 y) x (.f64 y x)) x))
	0.1b	(.f64 (-.f64 1 (.f64 x y)) x)
	42.6b	(cbrt.f64 (pow.f64 (-.f64 x (.f64 y (.f64 x x))) 3))
	36.5b	(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 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)))

Compiler

Compiled 898 to 415 computations (53.8% saved)

localize10.0ms (0.5%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (fma.f64 1 1 (neg.f64 (.f64 y x))) x)
✓	52.3b	(fma.f64 (neg.f64 y) x (*.f64 y x))

series15.0ms (0.7%)

Counts

2 → 48

Calls

2 calls:

8.0ms	(fma.f64 (neg.f64 y) x (*.f64 y x))
7.0ms	(.f64 (fma.f64 1 1 (neg.f64 (.f64 y x))) x)

rewrite4.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

2 → 30

Calls

2 calls:

2.0ms	(.f64 (fma.f64 1 1 (neg.f64 (.f64 y x))) x)
0.0ms	(fma.f64 (neg.f64 y) x (*.f64 y x))

simplify88.0ms (4.4%)

Algorithm

1×	egg-herbie

Rules

818×	`fma-def_binary64`
640×	`distribute-rgt-in_binary64`
588×	`distribute-lft-in_binary64`
390×	`distribute-neg-out_binary64`
231×	`associate-l_binary64`

Counts

78 → 57

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	55	703
1	103	588
2	289	532
3	919	532
4	3223	532
5	4764	532
6	4997	532
7	4847	532

prune45.0ms (2.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	56	1	57
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	57	7	64

Error

0.0b

Counts

64 → 7

Alt Table

Status	Error	Program
	42.6b	(cbrt.f64 (pow.f64 (-.f64 x (.f64 y (.f64 x x))) 3))
	1.4b	(+.f64 (.f64 (.f64 (-.f64 1 (.f64 x y)) (.f64 (cbrt.f64 x) (cbrt.f64 x))) (cbrt.f64 x)) (.f64 (fma.f64 (neg.f64 y) x (.f64 y x)) x))
	1.4b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (cbrt.f64 x) (-.f64 1 (.f64 x y))))
	10.3b	(-.f64 x (*.f64 y (pow.f64 x 2)))
✓	0.1b	(+.f64 (.f64 (fma.f64 1 1 (neg.f64 (.f64 y x))) x) (.f64 (fma.f64 (neg.f64 y) x (.f64 y x)) x))
▶	0.1b	(.f64 (-.f64 1 (.f64 x y)) x)
	36.5b	(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (-.f64 1 (*.f64 x y))))

Compiler

Compiled 1504 to 560 computations (62.8% saved)

localize4.0ms (0.2%)

Local error

Found 1 expressions with local error:

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

series7.0ms (0.4%)

Counts

1 → 24

Calls

1 calls:

7.0ms

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

rewrite5.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

5×	`add-sqr-sqrt_binary64`
3×	`associate-r_binary64`
3×	`associate-l_binary64`
3×	`*-un-lft-identity_binary64`
3×	`add-cube-cbrt_binary64`

Counts

1 → 22

Calls

1 calls:

4.0ms

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

simplify71.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

899×	`fma-def_binary64`
530×	`distribute-rgt-in_binary64`
503×	`distribute-lft-in_binary64`
290×	`fma-neg_binary64`
287×	`associate-l_binary64`

Counts

46 → 39

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	50	545
1	120	503
2	344	502
3	1111	500
4	3611	500
5	4567	500
6	4888	500

prune25.0ms (1.3%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	39	0	39
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	39	7	46

Error

0.0b

Counts

46 → 7

Alt Table

Status	Error	Program
	42.6b	(cbrt.f64 (pow.f64 (-.f64 x (.f64 y (.f64 x x))) 3))
	1.4b	(+.f64 (.f64 (.f64 (-.f64 1 (.f64 x y)) (.f64 (cbrt.f64 x) (cbrt.f64 x))) (cbrt.f64 x)) (.f64 (fma.f64 (neg.f64 y) x (.f64 y x)) x))
▶	1.4b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (cbrt.f64 x) (-.f64 1 (.f64 x y))))
	10.3b	(-.f64 x (*.f64 y (pow.f64 x 2)))
✓	0.1b	(+.f64 (.f64 (fma.f64 1 1 (neg.f64 (.f64 y x))) x) (.f64 (fma.f64 (neg.f64 y) x (.f64 y x)) x))
✓	0.1b	(.f64 (-.f64 1 (.f64 x y)) x)
	36.5b	(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (-.f64 1 (*.f64 x y))))

Compiler

Compiled 705 to 342 computations (51.5% saved)

localize7.0ms (0.4%)

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)

series153.0ms (7.7%)

Counts

4 → 72

Calls

4 calls:

65.0ms	(.f64 (cbrt.f64 x) (-.f64 1 (.f64 x y)))
38.0ms	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
35.0ms	(cbrt.f64 x)
15.0ms	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (cbrt.f64 x) (-.f64 1 (.f64 x y))))

rewrite32.0ms (1.6%)

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:

9.0ms	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (cbrt.f64 x) (-.f64 1 (.f64 x y))))
7.0ms	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
6.0ms	(.f64 (cbrt.f64 x) (-.f64 1 (.f64 x y)))
1.0ms	(cbrt.f64 x)

simplify137.0ms (6.9%)

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

prune112.0ms (5.6%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	227	4	231
Fresh	1	3	4
Picked	1	0	1
Done	0	2	2
Total	229	9	238

Error

Counts

238 → 9

Alt Table

Status	Error	Program
	10.3b	(-.f64 x (*.f64 y (pow.f64 x 2)))
	1.4b	(.f64 (.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (cbrt.f64 x)) (-.f64 1 (.f64 x y)))
✓	0.1b	(+.f64 (.f64 (fma.f64 1 1 (neg.f64 (.f64 y x))) x) (.f64 (fma.f64 (neg.f64 y) x (.f64 y x)) x))
	36.6b	(.f64 (.f64 (cbrt.f64 (sqrt.f64 x)) (sqrt.f64 x)) (.f64 (cbrt.f64 x) (-.f64 1 (.f64 x y))))
✓	0.1b	(.f64 (-.f64 1 (.f64 x y)) x)
	42.6b	(cbrt.f64 (pow.f64 (-.f64 x (.f64 y (.f64 x x))) 3))
	1.4b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 (.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (cbrt.f64 x)))) (.f64 (cbrt.f64 x) (-.f64 1 (.f64 x y))))
	36.5b	(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (-.f64 1 (*.f64 x y))))
	36.8b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (.f64 (sqrt.f64 (cbrt.f64 x)) (sqrt.f64 (cbrt.f64 x))) (-.f64 1 (*.f64 x y))))

Compiler

Compiled 4759 to 1721 computations (63.8% saved)

regimes243.0ms (12.1%)

Accuracy

Total 0.1b remaining (76.2%)

Threshold costs 0.1b (76.2%)

Counts

78 → 1

Compiler

Compiled 4333 to 2587 computations (40.3% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	28
1	26	28
2	34	28
3	38	28
4	39	28
5	38	28

end111.0ms (5.6%)

Compiler: Compiled 183 to 107 computations (41.5% 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

analyze79.0ms (4%)

sample710.0ms (35.5%)

simplify17.0ms (0.8%)

prune1.0ms (0.1%)

localize4.0ms (0.2%)

series7.0ms (0.4%)

rewrite6.0ms (0.3%)

simplify64.0ms (3.2%)

prune39.0ms (1.9%)

localize10.0ms (0.5%)

series15.0ms (0.7%)

rewrite4.0ms (0.2%)

simplify88.0ms (4.4%)

prune45.0ms (2.3%)

localize4.0ms (0.2%)

series7.0ms (0.4%)

rewrite5.0ms (0.2%)

simplify71.0ms (3.6%)

prune25.0ms (1.3%)

localize7.0ms (0.4%)

series153.0ms (7.7%)

rewrite32.0ms (1.6%)

simplify137.0ms (6.9%)

prune112.0ms (5.6%)

regimes243.0ms (12.1%)

simplify2.0ms (0.1%)

end111.0ms (5.6%)

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