Details

analyze80.0ms (3.1%)

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)

sample731.0ms (28.2%)

Results

678.0ms	8256×	body	128	valid
8.0ms	97×	body	128	invalid

Compiler

Compiled 29 to 20 computations (31% saved)

simplify17.0ms (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

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)))

series6.0ms (0.2%)

Counts

1 → 24

Calls

1 calls:

6.0ms

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

rewrite6.0ms (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:

4.0ms

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

simplify58.0ms (2.2%)

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

prune42.0ms (1.6%)

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
	35.2b	(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (-.f64 1 (*.f64 x y))))
	7.5b	(-.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)
	0.5b	(.f64 (.f64 x (.f64 (cbrt.f64 (-.f64 1 (.f64 x y))) (cbrt.f64 (-.f64 1 (.f64 x y))))) (cbrt.f64 (-.f64 1 (.f64 x y))))
	1.5b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (cbrt.f64 x) (-.f64 1 (.f64 x y))))
	9.1b	(/.f64 (.f64 x (-.f64 (.f64 1 1) (.f64 (.f64 x y) (.f64 x y)))) (+.f64 1 (.f64 x y)))
	13.3b	(/.f64 (.f64 x (-.f64 1 (pow.f64 (.f64 x y) 3))) (+.f64 (.f64 1 1) (+.f64 (.f64 (.f64 x y) (.f64 x y)) (.f64 1 (.f64 x y)))))

Compiler

Compiled 980 to 463 computations (52.8% saved)

localize10.0ms (0.4%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (fma.f64 1 1 (neg.f64 (.f64 y x))) x)
✓	51.3b	(fma.f64 (neg.f64 y) x (*.f64 y x))

series15.0ms (0.6%)

Counts

2 → 48

Calls

2 calls:

9.0ms	(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:

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

simplify89.0ms (3.5%)

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

prune57.0ms (2.2%)

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
	35.2b	(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (-.f64 1 (*.f64 x y))))
	7.5b	(-.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)
	0.5b	(.f64 (.f64 x (.f64 (cbrt.f64 (-.f64 1 (.f64 x y))) (cbrt.f64 (-.f64 1 (.f64 x y))))) (cbrt.f64 (-.f64 1 (.f64 x y))))
	1.5b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (cbrt.f64 x) (-.f64 1 (.f64 x y))))
	9.1b	(/.f64 (.f64 x (-.f64 (.f64 1 1) (.f64 (.f64 x y) (.f64 x y)))) (+.f64 1 (.f64 x y)))
	13.3b	(/.f64 (.f64 x (-.f64 1 (pow.f64 (.f64 x y) 3))) (+.f64 (.f64 1 1) (+.f64 (.f64 (.f64 x y) (.f64 x y)) (.f64 1 (.f64 x y)))))

Compiler

Compiled 1576 to 604 computations (61.7% 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)

series6.0ms (0.2%)

Counts

1 → 24

Calls

1 calls:

6.0ms

(*.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 (2.7%)

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

prune33.0ms (1.3%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	39	0	39
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	39	8	47

Error

0.0b

Counts

47 → 8

Alt Table

Status	Error	Program
	35.2b	(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (-.f64 1 (*.f64 x y))))
	7.5b	(-.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)
▶	0.5b	(.f64 (.f64 x (.f64 (cbrt.f64 (-.f64 1 (.f64 x y))) (cbrt.f64 (-.f64 1 (.f64 x y))))) (cbrt.f64 (-.f64 1 (.f64 x y))))
	1.5b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (cbrt.f64 x) (-.f64 1 (.f64 x y))))
	9.1b	(/.f64 (.f64 x (-.f64 (.f64 1 1) (.f64 (.f64 x y) (.f64 x y)))) (+.f64 1 (.f64 x y)))
	13.3b	(/.f64 (.f64 x (-.f64 1 (pow.f64 (.f64 x y) 3))) (+.f64 (.f64 1 1) (+.f64 (.f64 (.f64 x y) (.f64 x y)) (.f64 1 (.f64 x y)))))

Compiler

Compiled 777 to 386 computations (50.3% saved)

localize8.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 x (.f64 (cbrt.f64 (-.f64 1 (.f64 x y))) (cbrt.f64 (-.f64 1 (.f64 x y)))))
✓	0.1b	(.f64 (.f64 x (.f64 (cbrt.f64 (-.f64 1 (.f64 x y))) (cbrt.f64 (-.f64 1 (.f64 x y))))) (cbrt.f64 (-.f64 1 (.f64 x y))))
✓	0.2b	(cbrt.f64 (-.f64 1 (*.f64 x y)))
✓	0.2b	(.f64 (cbrt.f64 (-.f64 1 (.f64 x y))) (cbrt.f64 (-.f64 1 (*.f64 x y))))

series81.0ms (3.1%)

Counts

4 → 96

Calls

4 calls:

32.0ms	(.f64 x (.f64 (cbrt.f64 (-.f64 1 (.f64 x y))) (cbrt.f64 (-.f64 1 (.f64 x y)))))
25.0ms	(.f64 (cbrt.f64 (-.f64 1 (.f64 x y))) (cbrt.f64 (-.f64 1 (*.f64 x y))))
18.0ms	(cbrt.f64 (-.f64 1 (*.f64 x y)))
7.0ms	(.f64 (.f64 x (.f64 (cbrt.f64 (-.f64 1 (.f64 x y))) (cbrt.f64 (-.f64 1 (.f64 x y))))) (cbrt.f64 (-.f64 1 (.f64 x y))))

rewrite48.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Rules

80×	`cbrt-div_binary64`
44×	`associate-*r/_binary64`
40×	`flip--_binary64`
40×	`flip3--_binary64`
36×	`frac-times_binary64`

Counts

4 → 146

Calls

4 calls:

14.0ms	(.f64 (.f64 x (.f64 (cbrt.f64 (-.f64 1 (.f64 x y))) (cbrt.f64 (-.f64 1 (.f64 x y))))) (cbrt.f64 (-.f64 1 (.f64 x y))))
8.0ms	(.f64 x (.f64 (cbrt.f64 (-.f64 1 (.f64 x y))) (cbrt.f64 (-.f64 1 (.f64 x y)))))
7.0ms	(.f64 (cbrt.f64 (-.f64 1 (.f64 x y))) (cbrt.f64 (-.f64 1 (*.f64 x y))))
2.0ms	(cbrt.f64 (-.f64 1 (*.f64 x y)))

simplify166.0ms (6.4%)

Algorithm

1×	egg-herbie

Rules

373×	`associate-l_binary64`
328×	`distribute-neg-frac_binary64`
325×	`associate-r_binary64`
324×	`associate-/r*_binary64`
268×	`sub-neg_binary64`

Counts

242 → 334

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	391	8465
1	1100	7636
2	3705	7166
3	5208	7166

prune582.0ms (22.5%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	462	2	464
Fresh	2	3	5
Picked	0	1	1
Done	1	1	2
Total	465	7	472

Error

Counts

472 → 7

Alt Table

Status	Error	Program
	35.2b	(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (-.f64 1 (*.f64 x y))))
	7.5b	(-.f64 x (*.f64 y (pow.f64 x 2)))
	13.3b	(/.f64 (.f64 x (-.f64 1 (pow.f64 (.f64 y x) 3))) (fma.f64 (*.f64 y x) (fma.f64 y x 1) 1))
✓	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))
	0.5b	(.f64 (.f64 (.f64 x (.f64 (cbrt.f64 (-.f64 1 (.f64 x y))) (cbrt.f64 (-.f64 1 (.f64 x y))))) (cbrt.f64 (.f64 (cbrt.f64 (-.f64 1 (.f64 x y))) (cbrt.f64 (-.f64 1 (.f64 x y)))))) (cbrt.f64 (cbrt.f64 (-.f64 1 (.f64 x y)))))
✓	0.5b	(.f64 (.f64 x (.f64 (cbrt.f64 (-.f64 1 (.f64 x y))) (cbrt.f64 (-.f64 1 (.f64 x y))))) (cbrt.f64 (-.f64 1 (.f64 x y))))
	9.1b	(/.f64 (.f64 x (-.f64 (.f64 1 1) (.f64 (.f64 x y) (.f64 x y)))) (+.f64 1 (.f64 x y)))

Compiler

Compiled 18485 to 10784 computations (41.7% saved)

regimes354.0ms (13.7%)

Accuracy

Total 0.1b remaining (84.7%)

Threshold costs 0.1b (84.7%)

Counts

91 → 1

Compiler

Compiled 6823 to 4293 computations (37.1% 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

end105.0ms (4.1%)

Compiler: Compiled 191 to 115 computations (39.8% 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

analyze80.0ms (3.1%)

sample731.0ms (28.2%)

simplify17.0ms (0.7%)

prune2.0ms (0.1%)

localize4.0ms (0.2%)

series6.0ms (0.2%)

rewrite6.0ms (0.2%)

simplify58.0ms (2.2%)

prune42.0ms (1.6%)

localize10.0ms (0.4%)

series15.0ms (0.6%)

rewrite4.0ms (0.2%)

simplify89.0ms (3.5%)

prune57.0ms (2.2%)

localize4.0ms (0.2%)

series6.0ms (0.2%)

rewrite5.0ms (0.2%)

simplify71.0ms (2.7%)

prune33.0ms (1.3%)

localize8.0ms (0.3%)

series81.0ms (3.1%)

rewrite48.0ms (1.8%)

simplify166.0ms (6.4%)

prune582.0ms (22.5%)

regimes354.0ms (13.7%)

simplify2.0ms (0.1%)

end105.0ms (4.1%)

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