Details

analyze1.7s (1.1%)

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
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
0%	93.6%	6.4%	7
0%	93.6%	6.4%	8
0%	91.3%	8.7%	9
0%	86.6%	13.4%	10
0%	85.8%	14.2%	11
0%	83.1%	16.9%	12
0%	80.6%	19.4%	13
0%	79.4%	20.6%	14

Compiler

Compiled 21 to 15 computations (28.6% saved)

sample2.9s (1.9%)

Results

806.0ms	5363×	body	128	valid
674.0ms	1144×	body	2048	valid
341.0ms	409×	body	8192	exit
332.0ms	713×	body	1024	valid
308.0ms	418×	body	4096	valid
155.0ms	422×	body	512	valid
137.0ms	925×	body	128	invalid
49.0ms	196×	body	256	valid

Compiler

Compiled 41 to 29 computations (29.3% saved)

simplify382.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

2009×	`fma-neg_binary64`
1508×	`div-sub_binary64`
1334×	`associate-/l*_binary64`
1156×	`fma-def_binary64`
685×	`associate-/l/_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	26
1	34	22
2	64	22
3	132	22
4	198	22
5	325	22
6	552	22
7	918	22
8	1352	22
9	1554	22
10	2359	22
11	3158	22
12	2565	22
13	2653	22
14	3219	22
15	3361	22
16	3461	22
17	3985	22
18	4171	22
19	4439	22
20	4659	22
21	4701	22
22	4757	22
23	4941	22
24	4941	22
25	3365	22
26	3059	22
27	2983	22
28	2985	22
29	2997	22
30	2997	22
31	2997	22
32	2997	22
33	2736	22

prune4.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

34.7b

Counts

3 → 2

Alt Table

Status	Error	Program
	34.8b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
▶	34.8b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (.f64 2 a))

Compiler

Compiled 111 to 74 computations (33.3% saved)

localize11.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (.f64 2 a))
✓	0.8b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
✓	1.2b	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
✓	24.9b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

series207.0ms (0.1%)

Counts

4 → 96

Calls

4 calls:

93.0ms	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (.f64 2 a))
57.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
46.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
11.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

rewrite34.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`*-un-lft-identity_binary64`
11×	`add-sqr-sqrt_binary64`
10×	`fma-def_binary64`
10×	`add-cube-cbrt_binary64`
10×	`add-log-exp_binary64`

Counts

4 → 90

Calls

4 calls:

15.0ms	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (.f64 2 a))
7.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
3.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

simplify125.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

697×	`fma-neg_binary64`
327×	`cancel-sign-sub-inv_binary64`
226×	`distribute-rgt-neg-in_binary64`
150×	`distribute-rgt-neg-out_binary64`
146×	`associate-r_binary64`

Counts

186 → 207

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	243	4202
1	693	3825
2	2488	3724
3	4652	3704
4	4985	3704

prune172.0ms (0.1%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	197	10	207
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	198	11	209

Error

7.5b

Counts

209 → 11

Alt Table

Status	Error	Program
	48.4b	(/.f64 (neg.f64 b) a)
	56.7b	(/.f64 (+.f64 (neg.f64 b) b) (*.f64 2 a))
	35.1b	(/.f64 (exp.f64 (log.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b) b))) (*.f64 2 a))
	39.4b	(neg.f64 (/.f64 c b))
	34.8b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
	39.5b	(/.f64 (sqrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))))) (/.f64 a (/.f64 (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (*.f64 a -4))) b) b)) 2)))
	33.7b	(.f64 (/.f64 (.f64 (cbrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b) b)) (cbrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b) b))) 2) (/.f64 (cbrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b) b)) a))
▶	33.2b	(/.f64 (-.f64 b (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b)) (*.f64 a -2))
	44.8b	(exp.f64 (log.f64 (/.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b) b) (*.f64 a 2))))
	38.8b	(/.f64 (+.f64 (neg.f64 b) (exp.f64 (log.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b)))) (*.f64 2 a))
	40.6b	(/.f64 (cbrt.f64 (pow.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b) b) 3)) (*.f64 2 a))

Compiler

Compiled 5711 to 3216 computations (43.7% saved)

localize9.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b)
✓	0.1b	(/.f64 (-.f64 b (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b)) (*.f64 a -2))
✓	0.4b	(-.f64 b (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b))
✓	15.7b	(sqrt.f64 (.f64 c (.f64 a -4)))

series605.0ms (0.4%)

Counts

4 → 38

Calls

4 calls:

282.0ms	(/.f64 (-.f64 b (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b)) (*.f64 a -2))
180.0ms	(-.f64 b (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b))
121.0ms	(hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b)
21.0ms	(sqrt.f64 (.f64 c (.f64 a -4)))

rewrite17.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`*-un-lft-identity_binary64`
20×	`add-sqr-sqrt_binary64`
14×	`add-cube-cbrt_binary64`
10×	`pow1_binary64`
9×	`prod-diff_binary64`

Counts

4 → 84

Calls

4 calls:

6.0ms	(/.f64 (-.f64 b (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b)) (*.f64 a -2))
3.0ms	(-.f64 b (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b))
3.0ms	(sqrt.f64 (.f64 c (.f64 a -4)))
0.0ms	(hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b)

simplify127.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

675×	`fma-def_binary64`
343×	`fma-neg_binary64`
293×	`cancel-sign-sub-inv_binary64`
146×	`distribute-rgt-in_binary64`
144×	`distribute-rgt-neg-in_binary64`

Counts

122 → 199

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	245	3472
1	632	3007
2	2126	2816
3	4438	2808
4	4951	2808
5	4898	2808

prune176.0ms (0.1%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	194	5	199
Fresh	6	4	10
Picked	0	1	1
Done	0	0	0
Total	200	10	210

Error

3.5b

Counts

210 → 10

Alt Table

Status	Error	Program
	33.7b	(/.f64 (.f64 (cbrt.f64 (-.f64 b (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b))) (cbrt.f64 (-.f64 b (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b)))) (/.f64 a (/.f64 (cbrt.f64 (-.f64 b (hypot.f64 (sqrt.f64 (.f64 -4 (*.f64 c a))) b))) -2)))
	34.8b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
	39.5b	(/.f64 (sqrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))))) (/.f64 a (/.f64 (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (*.f64 a -4))) b) b)) 2)))
	33.6b	(/.f64 (+.f64 (fma.f64 (.f64 (cbrt.f64 b) (cbrt.f64 b)) (cbrt.f64 b) (neg.f64 (.f64 (cbrt.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b)) (.f64 (cbrt.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b)) (cbrt.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b)))))) (fma.f64 (neg.f64 (cbrt.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b))) (.f64 (cbrt.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b)) (cbrt.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b))) (.f64 (cbrt.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b)) (.f64 (cbrt.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b)) (cbrt.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b)))))) (*.f64 a -2))
	48.0b	(/.f64 (-.f64 b (hypot.f64 (.f64 (sqrt.f64 c) (sqrt.f64 (.f64 a -4))) b)) (*.f64 a -2))
✓	33.2b	(/.f64 (-.f64 b (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b)) (*.f64 a -2))
▶	33.3b	(/.f64 1 (/.f64 (.f64 a -2) (-.f64 b (hypot.f64 (sqrt.f64 (.f64 c (*.f64 a -4))) b))))
	56.7b	(/.f64 (-.f64 b b) (*.f64 a -2))
	48.4b	(/.f64 (neg.f64 b) a)
	39.4b	(neg.f64 (/.f64 c b))

Compiler

Compiled 5944 to 3877 computations (34.8% saved)

localize11.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (.f64 a -2) (-.f64 b (hypot.f64 (sqrt.f64 (.f64 c (*.f64 a -4))) b)))
✓	0.2b	(/.f64 1 (/.f64 (.f64 a -2) (-.f64 b (hypot.f64 (sqrt.f64 (.f64 c (*.f64 a -4))) b))))
	0.4b	(-.f64 b (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b))
	15.7b	(sqrt.f64 (.f64 c (.f64 a -4)))

series771.0ms (0.5%)

Counts

2 → 24

Calls

2 calls:

488.0ms	(/.f64 (.f64 a -2) (-.f64 b (hypot.f64 (sqrt.f64 (.f64 c (*.f64 a -4))) b)))
283.0ms	(/.f64 1 (/.f64 (.f64 a -2) (-.f64 b (hypot.f64 (sqrt.f64 (.f64 c (*.f64 a -4))) b))))

rewrite22.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

58×	`times-frac_binary64`
36×	`*-un-lft-identity_binary64`
36×	`add-sqr-sqrt_binary64`
28×	`add-exp-log_binary64`
24×	`add-cube-cbrt_binary64`

Counts

2 → 103

Calls

2 calls:

7.0ms	(/.f64 1 (/.f64 (.f64 a -2) (-.f64 b (hypot.f64 (sqrt.f64 (.f64 c (*.f64 a -4))) b))))
5.0ms	(/.f64 (.f64 a -2) (-.f64 b (hypot.f64 (sqrt.f64 (.f64 c (*.f64 a -4))) b)))

simplify99.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

738×	`associate-/r*_binary64`
443×	`associate-/r/_binary64`
382×	`fma-def_binary64`
309×	`associate-/l/_binary64`
154×	`cancel-sign-sub-inv_binary64`

Counts

127 → 194

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	223	4601
1	587	4063
2	1971	3995
3	5201	3995

prune255.0ms (0.2%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	279	3	282
Fresh	1	7	8
Picked	0	1	1
Done	1	0	1
Total	281	11	292

Error

3.5b

Counts

292 → 11

Alt Table

Status	Error	Program
	33.7b	(/.f64 (.f64 (cbrt.f64 (-.f64 b (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b))) (cbrt.f64 (-.f64 b (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b)))) (/.f64 a (/.f64 (cbrt.f64 (-.f64 b (hypot.f64 (sqrt.f64 (.f64 -4 (*.f64 c a))) b))) -2)))
	34.8b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
	39.5b	(/.f64 (sqrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))))) (/.f64 a (/.f64 (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (*.f64 a -4))) b) b)) 2)))
▶	33.6b	(/.f64 (+.f64 (fma.f64 (.f64 (cbrt.f64 b) (cbrt.f64 b)) (cbrt.f64 b) (neg.f64 (.f64 (cbrt.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b)) (.f64 (cbrt.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b)) (cbrt.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b)))))) (fma.f64 (neg.f64 (cbrt.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b))) (.f64 (cbrt.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b)) (cbrt.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b))) (.f64 (cbrt.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b)) (.f64 (cbrt.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b)) (cbrt.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b)))))) (*.f64 a -2))
	48.4b	(/.f64 (neg.f64 b) a)
	48.5b	(/.f64 1 (neg.f64 (/.f64 a b)))
	39.4b	(neg.f64 (/.f64 c b))
	45.2b	(/.f64 1 (fma.f64 4 (/.f64 (.f64 a b) (.f64 -4 (*.f64 c a))) (/.f64 a b)))
	48.0b	(/.f64 (-.f64 b (hypot.f64 (.f64 (sqrt.f64 c) (sqrt.f64 (.f64 a -4))) b)) (*.f64 a -2))
✓	33.3b	(/.f64 1 (/.f64 (.f64 a -2) (-.f64 b (hypot.f64 (sqrt.f64 (.f64 c (*.f64 a -4))) b))))
	48.0b	(/.f64 1 (/.f64 (.f64 a -2) (-.f64 b (hypot.f64 (.f64 (sqrt.f64 c) (sqrt.f64 (*.f64 -4 a))) b))))

Compiler

Compiled 8977 to 6010 computations (33.1% saved)

localize144.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.6b	(cbrt.f64 b)
✓	11.2b	(fma.f64 (.f64 (cbrt.f64 b) (cbrt.f64 b)) (cbrt.f64 b) (neg.f64 (.f64 (cbrt.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b)) (.f64 (cbrt.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b)) (cbrt.f64 (hypot.f64 (sqrt.f64 (.f64 c (*.f64 a -4))) b))))))
	15.7b	(sqrt.f64 (.f64 c (.f64 a -4)))
✓	44.7b	(fma.f64 (neg.f64 (cbrt.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b))) (.f64 (cbrt.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b)) (cbrt.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b))) (.f64 (cbrt.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b)) (.f64 (cbrt.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b)) (cbrt.f64 (hypot.f64 (sqrt.f64 (.f64 c (*.f64 a -4))) b)))))

Details

analyze1.7s (1.1%)

sample2.9s (1.9%)

simplify382.0ms (0.3%)

prune4.0ms (0%)

localize11.0ms (0%)

series207.0ms (0.1%)

rewrite34.0ms (0%)

simplify125.0ms (0.1%)

prune172.0ms (0.1%)

localize9.0ms (0%)

series605.0ms (0.4%)

rewrite17.0ms (0%)

simplify127.0ms (0.1%)

prune176.0ms (0.1%)

localize11.0ms (0%)

series771.0ms (0.5%)

rewrite22.0ms (0%)

simplify99.0ms (0.1%)

prune255.0ms (0.2%)

localize144.0ms (0.1%)

series2.4min (94.8%)

Profiling