Details

analyze108.0ms (4.9%)

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)

sample788.0ms (35.8%)

Results

731.0ms	8256×	body	128	valid
7.0ms	87×	body	128	invalid

Compiler

Compiled 29 to 20 computations (31% saved)

simplify16.0ms (0.7%)

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

prune4.0ms (0.2%)

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)))

series6.0ms (0.3%)

Counts

1 → 24

Calls

1 calls:

5.0ms

(*.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)))

simplify62.0ms (2.8%)

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

prune42.0ms (1.9%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	43	8	51
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	44	8	52

Error

0.0b

Counts

52 → 8

Alt Table

Status	Error	Program
	8.9b	(.f64 (.f64 x (sqrt.f64 (-.f64 1 (.f64 x y)))) (sqrt.f64 (-.f64 1 (.f64 x y))))
	33.0b	(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (-.f64 1 (*.f64 x y))))
	1.5b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (cbrt.f64 x) (-.f64 1 (.f64 x y))))
	7.3b	(/.f64 (.f64 x (-.f64 (.f64 1 1) (.f64 (.f64 x y) (.f64 x y)))) (+.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))
	39.5b	(cbrt.f64 (.f64 (.f64 (.f64 x (-.f64 1 (.f64 x y))) (.f64 x (-.f64 1 (.f64 x y)))) (.f64 x (-.f64 1 (.f64 x y)))))
	9.3b	(-.f64 x (*.f64 y (pow.f64 x 2)))

Compiler

Compiled 966 to 455 computations (52.9% 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)
✓	53.0b	(fma.f64 (neg.f64 y) x (*.f64 y x))

series18.0ms (0.8%)

Counts

2 → 48

Calls

2 calls:

12.0ms	(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))

simplify92.0ms (4.2%)

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

prune75.0ms (3.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	57	0	57
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	57	8	65

Error

0.0b

Counts

65 → 8

Alt Table

Status	Error	Program
	8.9b	(.f64 (.f64 x (sqrt.f64 (-.f64 1 (.f64 x y)))) (sqrt.f64 (-.f64 1 (.f64 x y))))
	33.0b	(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (-.f64 1 (*.f64 x y))))
	1.5b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (cbrt.f64 x) (-.f64 1 (.f64 x y))))
	7.3b	(/.f64 (.f64 x (-.f64 (.f64 1 1) (.f64 (.f64 x y) (.f64 x y)))) (+.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))
	39.5b	(cbrt.f64 (.f64 (.f64 (.f64 x (-.f64 1 (.f64 x y))) (.f64 x (-.f64 1 (.f64 x y)))) (.f64 x (-.f64 1 (.f64 x y)))))
	9.3b	(-.f64 x (*.f64 y (pow.f64 x 2)))

Compiler

Compiled 1562 to 596 computations (61.8% 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))
✓	0.2b	(.f64 (neg.f64 (.f64 x y)) x)

series17.0ms (0.8%)

Counts

2 → 48

Calls

2 calls:

11.0ms	(.f64 (neg.f64 (.f64 x y)) x)
6.0ms	(+.f64 (.f64 1 x) (.f64 (neg.f64 (*.f64 x y)) x))

rewrite11.0ms (0.5%)

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:

7.0ms	(.f64 (neg.f64 (.f64 x y)) x)
3.0ms	(+.f64 (.f64 1 x) (.f64 (neg.f64 (*.f64 x y)) x))

simplify93.0ms (4.2%)

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

prune65.0ms (3%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	69	1	70
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	69	9	78

Error

Counts

78 → 9

Alt Table

Status	Error	Program
	8.9b	(.f64 (.f64 x (sqrt.f64 (-.f64 1 (.f64 x y)))) (sqrt.f64 (-.f64 1 (.f64 x y))))
	33.0b	(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (-.f64 1 (*.f64 x y))))
▶	1.5b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (cbrt.f64 x) (-.f64 1 (.f64 x y))))
	34.3b	(+.f64 (.f64 1 x) (.f64 (*.f64 y (neg.f64 (pow.f64 x 3/2))) (sqrt.f64 x)))
	7.3b	(/.f64 (.f64 x (-.f64 (.f64 1 1) (.f64 (.f64 x y) (.f64 x y)))) (+.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))
	39.5b	(cbrt.f64 (.f64 (.f64 (.f64 x (-.f64 1 (.f64 x y))) (.f64 x (-.f64 1 (.f64 x y)))) (.f64 x (-.f64 1 (.f64 x y)))))
	9.3b	(-.f64 x (*.f64 y (pow.f64 x 2)))

Compiler

Compiled 1325 to 550 computations (58.5% saved)

localize7.0ms (0.3%)

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)

series205.0ms (9.3%)

Counts

4 → 72

Calls

4 calls:

114.0ms	(.f64 (cbrt.f64 x) (-.f64 1 (.f64 x y)))
38.0ms	(cbrt.f64 x)
37.0ms	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
16.0ms	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (cbrt.f64 x) (-.f64 1 (.f64 x y))))

rewrite33.0ms (1.5%)

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 (cbrt.f64 x) (-.f64 1 (.f64 x y)))
8.0ms	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (cbrt.f64 x) (-.f64 1 (.f64 x y))))
4.0ms	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
3.0ms	(cbrt.f64 x)

simplify149.0ms (6.8%)

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

prune104.0ms (4.7%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	231	0	231
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	231	9	240

Error

Counts

240 → 9

Alt Table

Status	Error	Program
	8.9b	(.f64 (.f64 x (sqrt.f64 (-.f64 1 (.f64 x y)))) (sqrt.f64 (-.f64 1 (.f64 x y))))
	33.0b	(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (-.f64 1 (*.f64 x y))))
✓	1.5b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (cbrt.f64 x) (-.f64 1 (.f64 x y))))
	34.3b	(+.f64 (.f64 1 x) (.f64 (*.f64 y (neg.f64 (pow.f64 x 3/2))) (sqrt.f64 x)))
	7.3b	(/.f64 (.f64 x (-.f64 (.f64 1 1) (.f64 (.f64 x y) (.f64 x y)))) (+.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))
	39.5b	(cbrt.f64 (.f64 (.f64 (.f64 x (-.f64 1 (.f64 x y))) (.f64 x (-.f64 1 (.f64 x y)))) (.f64 x (-.f64 1 (.f64 x y)))))
	9.3b	(-.f64 x (*.f64 y (pow.f64 x 2)))

Compiler

Compiled 4768 to 1730 computations (63.7% saved)

regimes145.0ms (6.6%)

Accuracy

Total 0.1b remaining (85.3%)

Threshold costs 0.1b (85.3%)

Counts

39 → 1

Compiler

Compiled 1984 to 1282 computations (35.4% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	25
1	25	25
2	34	25
3	39	25
4	41	25
5	40	25

end128.0ms (5.8%)

Compiler: Compiled 188 to 112 computations (40.4% 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

analyze108.0ms (4.9%)

sample788.0ms (35.8%)

simplify16.0ms (0.7%)

prune4.0ms (0.2%)

localize4.0ms (0.2%)

series6.0ms (0.3%)

rewrite6.0ms (0.3%)

simplify62.0ms (2.8%)

prune42.0ms (1.9%)

localize10.0ms (0.5%)

series18.0ms (0.8%)

rewrite4.0ms (0.2%)

simplify92.0ms (4.2%)

prune75.0ms (3.4%)

localize6.0ms (0.3%)

series17.0ms (0.8%)

rewrite11.0ms (0.5%)

simplify93.0ms (4.2%)

prune65.0ms (3%)

localize7.0ms (0.3%)

series205.0ms (9.3%)

rewrite33.0ms (1.5%)

simplify149.0ms (6.8%)

prune104.0ms (4.7%)

regimes145.0ms (6.6%)

simplify3.0ms (0.1%)

end128.0ms (5.8%)

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