Details

analyze86.0ms (2.5%)

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)

sample914.0ms (26.8%)

Results

856.0ms	8256×	body	128	valid
8.0ms	94×	body	128	invalid

Compiler

Compiled 29 to 20 computations (31% saved)

simplify19.0ms (0.5%)

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%)

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 (0.1%)

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)))

rewrite13.0ms (0.4%)

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:

12.0ms

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

simplify56.0ms (1.6%)

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 (1.2%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	46	5	51
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	46	6	52

Error

0.0b

Counts

52 → 6

Alt Table

Status	Error	Program
	1.4b	(.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)))))
	0.5b	(.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))))
	7.3b	(-.f64 x (*.f64 y (pow.f64 x 2)))
	6.1b	(/.f64 (.f64 x (-.f64 (.f64 1 1) (.f64 (.f64 x y) (.f64 x y)))) (+.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))
✓	0.1b	(.f64 x (-.f64 1 (.f64 x y)))

Compiler

Compiled 911 to 423 computations (53.6% saved)

localize12.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (fma.f64 1 1 (neg.f64 (.f64 y x))) x)
✓	52.7b	(fma.f64 (neg.f64 y) x (*.f64 y x))

series15.0ms (0.4%)

Counts

2 → 48

Calls

2 calls:

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

rewrite4.0ms (0.1%)

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))

simplify89.0ms (2.6%)

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

prune48.0ms (1.4%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	56	1	57
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	57	6	63

Error

0.0b

Counts

63 → 6

Alt Table

Status	Error	Program
▶	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))))
	33.8b	(+.f64 (.f64 (.f64 (-.f64 1 (.f64 x y)) (sqrt.f64 x)) (sqrt.f64 x)) (.f64 (fma.f64 (neg.f64 y) x (*.f64 y x)) x))
	7.3b	(-.f64 x (*.f64 y (pow.f64 x 2)))
	6.1b	(/.f64 (.f64 x (-.f64 (.f64 1 1) (.f64 (.f64 x y) (.f64 x y)))) (+.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))
✓	0.1b	(.f64 x (-.f64 1 (.f64 x y)))

Compiler

Compiled 1497 to 556 computations (62.9% saved)

localize7.0ms (0.2%)

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)))))
✓	0.2b	(.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))))

series90.0ms (2.7%)

Counts

4 → 96

Calls

4 calls:

39.0ms	(.f64 x (.f64 (cbrt.f64 (-.f64 1 (.f64 x y))) (cbrt.f64 (-.f64 1 (.f64 x y)))))
27.0ms	(.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))))

rewrite51.0ms (1.5%)

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:

13.0ms	(.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))))
9.0ms	(.f64 x (.f64 (cbrt.f64 (-.f64 1 (.f64 x y))) (cbrt.f64 (-.f64 1 (.f64 x y)))))
8.0ms	(.f64 (cbrt.f64 (-.f64 1 (.f64 x y))) (cbrt.f64 (-.f64 1 (*.f64 x y))))
2.0ms	(cbrt.f64 (-.f64 1 (*.f64 x y)))

simplify168.0ms (4.9%)

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

prune559.0ms (16.4%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	463	1	464
Fresh	1	2	3
Picked	0	1	1
Done	0	2	2
Total	464	6	470

Error

Counts

470 → 6

Alt Table

Status	Error	Program
✓	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))))
▶	0.5b	(.f64 (.f64 x (.f64 (.f64 (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)))))) (cbrt.f64 (-.f64 1 (.f64 x y))))
	7.3b	(-.f64 x (*.f64 y (pow.f64 x 2)))
	6.1b	(/.f64 (.f64 x (-.f64 (.f64 1 1) (.f64 (.f64 x y) (.f64 x y)))) (+.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))
✓	0.1b	(.f64 x (-.f64 1 (.f64 x y)))

Compiler

Compiled 18530 to 10812 computations (41.7% saved)

localize13.0ms (0.4%)

Local error

Found 4 expressions with local error:

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

series42.0ms (1.2%)

Counts

2 → 48

Calls

2 calls:

24.0ms	(cbrt.f64 (.f64 (cbrt.f64 (-.f64 1 (.f64 x y))) (cbrt.f64 (-.f64 1 (*.f64 x y)))))
18.0ms	(cbrt.f64 (cbrt.f64 (-.f64 1 (*.f64 x y))))

rewrite16.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`cbrt-div_binary64`
10×	`cbrt-prod_binary64`
7×	`flip--_binary64`
7×	`flip3--_binary64`
4×	`*-un-lft-identity_binary64`

Counts

2 → 37

Calls

2 calls:

11.0ms	(cbrt.f64 (.f64 (cbrt.f64 (-.f64 1 (.f64 x y))) (cbrt.f64 (-.f64 1 (*.f64 x y)))))
2.0ms	(cbrt.f64 (cbrt.f64 (-.f64 1 (*.f64 x y))))

simplify104.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

717×	`cancel-sign-sub-inv_binary64`
672×	`fma-neg_binary64`
294×	`distribute-rgt-neg-in_binary64`
288×	`associate-/r*_binary64`
271×	`distribute-lft-neg-in_binary64`

Counts

85 → 132

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	250	3406
1	676	3184
2	2342	2728
3	4328	2558
4	4971	2558

prune774.0ms (22.7%)

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	566	0	566
Fresh	0	2	2
Picked	0	1	1
Done	0	3	3
Total	566	6	572

Error

Counts

572 → 6

Alt Table

Status	Error	Program
✓	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))))
✓	0.5b	(.f64 (.f64 x (.f64 (.f64 (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)))))) (cbrt.f64 (-.f64 1 (.f64 x y))))
	7.3b	(-.f64 x (*.f64 y (pow.f64 x 2)))
	6.1b	(/.f64 (.f64 x (-.f64 (.f64 1 1) (.f64 (.f64 x y) (.f64 x y)))) (+.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))
✓	0.1b	(.f64 x (-.f64 1 (.f64 x y)))

Compiler

Compiled 31824 to 19014 computations (40.3% saved)

regimes171.0ms (5%)

Accuracy

Total 0.1b remaining (76%)

Threshold costs 0.1b (76%)

Counts

50 → 1

Compiler

Compiled 3577 to 2239 computations (37.4% saved)

simplify3.0ms (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	14	28
1	28	28
2	36	28
3	40	28
4	41	28
5	38	28

end100.0ms (2.9%)

Compiler: Compiled 166 to 100 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

analyze86.0ms (2.5%)

sample914.0ms (26.8%)

simplify19.0ms (0.5%)

prune1.0ms (0%)

localize4.0ms (0.1%)

series6.0ms (0.2%)

rewrite13.0ms (0.4%)

simplify56.0ms (1.6%)

prune42.0ms (1.2%)

localize12.0ms (0.3%)

series15.0ms (0.4%)

rewrite4.0ms (0.1%)

simplify89.0ms (2.6%)

prune48.0ms (1.4%)

localize7.0ms (0.2%)

series90.0ms (2.7%)

rewrite51.0ms (1.5%)

simplify168.0ms (4.9%)

prune559.0ms (16.4%)

localize13.0ms (0.4%)

series42.0ms (1.2%)

rewrite16.0ms (0.5%)

simplify104.0ms (3.1%)

prune774.0ms (22.7%)

regimes171.0ms (5%)

simplify3.0ms (0.1%)

end100.0ms (2.9%)

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