Details

analyze82.0ms (3.9%)

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
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)

sample736.0ms (34.7%)

Results

684.0ms	8256×	body	128	valid
7.0ms	95×	body	128	invalid

Compiler

Compiled 29 to 20 computations (31% saved)

simplify18.0ms (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

prune2.0ms (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)))

series8.0ms (0.4%)

Counts

1 → 24

Calls

1 calls:

8.0ms

(*.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)))

simplify57.0ms (2.7%)

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

prune100.0ms (4.7%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	46	5	51
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	47	5	52

Error

0.0b

Counts

52 → 5

Alt Table

Status	Error	Program
▶	0.1b	(+.f64 (.f64 1 x) (.f64 (neg.f64 (*.f64 x y)) x))
	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))
	33.8b	(.f64 (sqrt.f64 (.f64 x (-.f64 1 (.f64 x y)))) (sqrt.f64 (.f64 x (-.f64 1 (*.f64 x y)))))
	35.7b	(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (-.f64 1 (*.f64 x y))))
	1.3b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (cbrt.f64 x) (-.f64 1 (.f64 x y))))

Compiler

Compiled 858 to 391 computations (54.4% saved)

localize6.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 1 x) (.f64 (neg.f64 (*.f64 x y)) x))
✓	0.1b	(.f64 (neg.f64 (.f64 x y)) x)

series18.0ms (0.9%)

Counts

2 → 48

Calls

2 calls:

11.0ms	(.f64 (neg.f64 (.f64 x y)) x)
7.0ms	(+.f64 (.f64 1 x) (.f64 (neg.f64 (*.f64 x y)) x))

rewrite7.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`associate-l_binary64`
6×	`add-sqr-sqrt_binary64`
4×	`*-un-lft-identity_binary64`
4×	`add-cube-cbrt_binary64`
4×	`add-cbrt-cube_binary64`

Counts

2 → 40

Calls

2 calls:

3.0ms	(.f64 (neg.f64 (.f64 x y)) x)
3.0ms	(+.f64 (.f64 1 x) (.f64 (neg.f64 (*.f64 x y)) x))

simplify159.0ms (7.5%)

Algorithm

1×	egg-herbie

Rules

786×	`unsub-neg_binary64`
423×	`times-frac_binary64`
380×	`neg-sub0_binary64`
365×	`neg-mul-1_binary64`
320×	`distribute-lft-neg-out_binary64`

Counts

88 → 70

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	69	933
1	189	909
2	748	899
3	2086	893
4	3687	893
5	4607	893
6	5301	893

prune53.0ms (2.5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	69	1	70
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	69	6	75

Error

0.0b

Counts

75 → 6

Alt Table

Status	Error	Program
	39.3b	(/.f64 (+.f64 (pow.f64 (.f64 1 x) 3) (pow.f64 (.f64 (neg.f64 (.f64 x y)) x) 3)) (+.f64 (.f64 (.f64 1 x) (.f64 1 x)) (-.f64 (.f64 (.f64 (neg.f64 (.f64 x y)) x) (.f64 (neg.f64 (.f64 x y)) x)) (.f64 (.f64 1 x) (.f64 (neg.f64 (*.f64 x y)) x)))))
✓	0.1b	(+.f64 (.f64 1 x) (.f64 (neg.f64 (*.f64 x y)) x))
▶	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))
	33.8b	(.f64 (sqrt.f64 (.f64 x (-.f64 1 (.f64 x y)))) (sqrt.f64 (.f64 x (-.f64 1 (*.f64 x y)))))
	35.7b	(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (-.f64 1 (*.f64 x y))))
	1.3b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (cbrt.f64 x) (-.f64 1 (.f64 x y))))

Compiler

Compiled 1306 to 524 computations (59.9% 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)
✓	50.7b	(fma.f64 (neg.f64 y) x (*.f64 y x))

series15.0ms (0.7%)

Counts

2 → 48

Calls

2 calls:

9.0ms	(fma.f64 (neg.f64 y) x (*.f64 y x))
6.0ms	(.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:

3.0ms	(.f64 (fma.f64 1 1 (neg.f64 (.f64 y x))) x)
0.0ms	(fma.f64 (neg.f64 y) x (*.f64 y x))

simplify87.0ms (4.1%)

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

prune46.0ms (2.2%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	57	0	57
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	57	6	63

Error

0.0b

Counts

63 → 6

Alt Table

Status	Error	Program
	39.3b	(/.f64 (+.f64 (pow.f64 (.f64 1 x) 3) (pow.f64 (.f64 (neg.f64 (.f64 x y)) x) 3)) (+.f64 (.f64 (.f64 1 x) (.f64 1 x)) (-.f64 (.f64 (.f64 (neg.f64 (.f64 x y)) x) (.f64 (neg.f64 (.f64 x y)) x)) (.f64 (.f64 1 x) (.f64 (neg.f64 (*.f64 x y)) x)))))
✓	0.1b	(+.f64 (.f64 1 x) (.f64 (neg.f64 (*.f64 x y)) x))
✓	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))
	33.8b	(.f64 (sqrt.f64 (.f64 x (-.f64 1 (.f64 x y)))) (sqrt.f64 (.f64 x (-.f64 1 (*.f64 x y)))))
	35.7b	(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (-.f64 1 (*.f64 x y))))
▶	1.3b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (cbrt.f64 x) (-.f64 1 (.f64 x y))))

Compiler

Compiled 1540 to 572 computations (62.9% saved)

localize8.0ms (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))
✓	0.5b	(cbrt.f64 x)

series162.0ms (7.6%)

Counts

4 → 72

Calls

4 calls:

67.0ms	(.f64 (cbrt.f64 x) (-.f64 1 (.f64 x y)))
36.0ms	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
35.0ms	(cbrt.f64 x)
23.0ms	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (cbrt.f64 x) (-.f64 1 (.f64 x y))))

rewrite29.0ms (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:

10.0ms	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (cbrt.f64 x) (-.f64 1 (.f64 x y))))
5.0ms	(.f64 (cbrt.f64 x) (-.f64 1 (.f64 x y)))
4.0ms	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
1.0ms	(cbrt.f64 x)

simplify139.0ms (6.6%)

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

prune100.0ms (4.7%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	230	1	231
Fresh	1	2	3
Picked	0	1	1
Done	0	2	2
Total	231	6	237

Error

Counts

237 → 6

Alt Table

Status	Error	Program
	2.2b	(.f64 (.f64 (.f64 (.f64 (cbrt.f64 (cbrt.f64 x)) (cbrt.f64 (cbrt.f64 x))) (.f64 (cbrt.f64 (cbrt.f64 x)) (cbrt.f64 (cbrt.f64 x)))) (.f64 (cbrt.f64 (cbrt.f64 x)) (cbrt.f64 (cbrt.f64 x)))) (.f64 (cbrt.f64 x) (-.f64 1 (.f64 x y))))
✓	0.1b	(+.f64 (.f64 1 x) (.f64 (neg.f64 (*.f64 x y)) x))
✓	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))
	33.8b	(.f64 (sqrt.f64 (.f64 x (-.f64 1 (.f64 x y)))) (sqrt.f64 (.f64 x (-.f64 1 (*.f64 x y)))))
	35.7b	(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (-.f64 1 (*.f64 x y))))
✓	1.3b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (cbrt.f64 x) (-.f64 1 (.f64 x y))))

Compiler

Compiled 4733 to 1699 computations (64.1% saved)

regimes186.0ms (8.8%)

Accuracy

Total 0.1b remaining (61.2%)

Threshold costs 0.1b (61.2%)

Counts

67 → 1

Compiler

Compiled 3308 to 2038 computations (38.4% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	10
1	18	10
2	32	10
3	44	10
4	49	10
5	51	10
6	49	10

end76.0ms (3.6%)

Compiler: Compiled 133 to 71 computations (46.6% 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

analyze82.0ms (3.9%)

sample736.0ms (34.7%)

simplify18.0ms (0.8%)

prune2.0ms (0.1%)

localize4.0ms (0.2%)

series8.0ms (0.4%)

rewrite6.0ms (0.3%)

simplify57.0ms (2.7%)

prune100.0ms (4.7%)

localize6.0ms (0.3%)

series18.0ms (0.9%)

rewrite7.0ms (0.3%)

simplify159.0ms (7.5%)

prune53.0ms (2.5%)

localize10.0ms (0.5%)

series15.0ms (0.7%)

rewrite4.0ms (0.2%)

simplify87.0ms (4.1%)

prune46.0ms (2.2%)

localize8.0ms (0.4%)

series162.0ms (7.6%)

rewrite29.0ms (1.4%)

simplify139.0ms (6.6%)

prune100.0ms (4.7%)

regimes186.0ms (8.8%)

simplify3.0ms (0.1%)

end76.0ms (3.6%)

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