Details

analyze642.0ms (9.6%)

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
12.5%	87.4%	0.1%	5
18.7%	81.1%	0.1%	6
21.8%	71.8%	6.4%	7
31.2%	62.4%	6.4%	8
35.9%	55.4%	8.7%	9
37.8%	48.8%	13.4%	10
42.7%	42.3%	15%	11
47.7%	34.2%	18.1%	12
49.1%	30.4%	20.5%	13
51.9%	25.8%	22.3%	14

Compiler

Compiled 21 to 15 computations (28.6% saved)

sample2.3s (35%)

Results

714.0ms	5276×	body	128	valid
621.0ms	1212×	body	2048	valid
345.0ms	795×	body	1024	valid
267.0ms	423×	body	4096	valid
135.0ms	1082×	body	128	invalid
121.0ms	354×	body	512	valid
49.0ms	196×	body	256	valid

Compiler

Compiled 62 to 44 computations (29% saved)

simplify396.0ms (5.9%)

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 (0.1%)

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

38.2b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	38.2b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (.f64 2 a))
	38.3b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))

Compiler

Compiled 111 to 74 computations (33.3% saved)

localize11.0ms (0.2%)

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))
✓	0.4b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
✓	0.7b	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
✓	26.8b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

series129.0ms (1.9%)

Counts

4 → 96

Calls

4 calls:

56.0ms	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (.f64 2 a))
34.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
29.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
9.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

rewrite25.0ms (0.4%)

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:

9.0ms	(/.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)))))
3.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
3.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

simplify122.0ms (1.8%)

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

prune146.0ms (2.2%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	196	11	207
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	198	11	209

Error

4.9b

Counts

209 → 11

Alt Table

Status	Error	Program
	35.0b	(.f64 (/.f64 (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b) b)) 2) (/.f64 (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (*.f64 a -4))) b) b)) a))
	41.6b	(/.f64 (+.f64 (neg.f64 b) (exp.f64 (log.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b)))) (*.f64 2 a))
	55.2b	(/.f64 (+.f64 (neg.f64 b) b) (*.f64 2 a))
▶	34.9b	(/.f64 (-.f64 b (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b)) (*.f64 a -2))
	45.0b	(/.f64 (neg.f64 b) a)
	45.2b	(-.f64 (/.f64 c b) (/.f64 b a))
	35.4b	(.f64 (.f64 (cbrt.f64 (/.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b) b) (.f64 a 2))) (cbrt.f64 (/.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b) b) (.f64 a 2)))) (cbrt.f64 (/.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b) b) (*.f64 a 2))))
	36.3b	(neg.f64 (/.f64 c b))
	49.6b	(cbrt.f64 (pow.f64 (/.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b) b) (*.f64 a 2)) 3))
	37.3b	(/.f64 (/.f64 (.f64 4 (.f64 c a)) (-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b))) (*.f64 2 a))
	38.3b	(/.f64 1 (/.f64 (.f64 2 a) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))))))

Compiler

Compiled 5721 to 3222 computations (43.7% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (-.f64 b (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b)) (*.f64 a -2))
✓	0.2b	(-.f64 b (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b))
✓	13.5b	(sqrt.f64 (.f64 c (.f64 a -4)))

series260.0ms (3.9%)

Counts

3 → 24

Calls

3 calls:

150.0ms	(/.f64 (-.f64 b (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b)) (*.f64 a -2))
96.0ms	(-.f64 b (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b))
13.0ms	(sqrt.f64 (.f64 c (.f64 a -4)))

rewrite15.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`*-un-lft-identity_binary64`
19×	`add-sqr-sqrt_binary64`
13×	`add-cube-cbrt_binary64`
9×	`prod-diff_binary64`
9×	`pow1_binary64`

Counts

3 → 74

Calls

3 calls:

5.0ms	(/.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))
2.0ms	(sqrt.f64 (.f64 c (.f64 a -4)))

simplify71.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

822×	`associate-/r*_binary64`
545×	`fma-def_binary64`
225×	`cancel-sign-sub-inv_binary64`
153×	`fma-neg_binary64`
142×	`associate-/l/_binary64`

Counts

98 → 159

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	223	2931
1	562	2482
2	1923	2293
3	5131	2293

prune117.0ms (1.7%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	158	1	159
Fresh	2	8	10
Picked	0	1	1
Done	0	0	0
Total	160	10	170

Error

2.4b

Counts

170 → 10

Alt Table

Status	Error	Program
	49.3b	(/.f64 (-.f64 b (hypot.f64 (.f64 (sqrt.f64 c) (sqrt.f64 (.f64 a -4))) b)) (*.f64 a -2))
▶	35.0b	(.f64 (/.f64 (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b) b)) 2) (/.f64 (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (*.f64 a -4))) b) b)) a))
	41.6b	(/.f64 (+.f64 (neg.f64 b) (exp.f64 (log.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b)))) (*.f64 2 a))
	55.2b	(/.f64 (+.f64 (neg.f64 b) b) (*.f64 2 a))
✓	34.9b	(/.f64 (-.f64 b (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b)) (*.f64 a -2))
	45.0b	(/.f64 (neg.f64 b) a)
	36.3b	(neg.f64 (/.f64 c b))
	49.6b	(cbrt.f64 (pow.f64 (/.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b) b) (*.f64 a 2)) 3))
	37.3b	(/.f64 (/.f64 (.f64 4 (.f64 c a)) (-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b))) (*.f64 2 a))
	38.3b	(/.f64 1 (/.f64 (.f64 2 a) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))))))

Compiler

Compiled 4721 to 3085 computations (34.7% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b) b)) a)
✓	0.1b	(.f64 (/.f64 (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b) b)) 2) (/.f64 (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (*.f64 a -4))) b) b)) a))
✓	0.2b	(-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b) b)
	13.5b	(sqrt.f64 (.f64 c (.f64 a -4)))

series495.0ms (7.4%)

Counts

3 → 28

Calls

3 calls:

266.0ms

(/.f64 (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b) b)) a)

144.0ms

(*.f64 (/.f64 (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b) b)) 2) (/.f64 (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b) b)) a))

85.0ms

(-.f64 (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b) b)

rewrite51.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

110×	`add-sqr-sqrt_binary64`
84×	`times-frac_binary64`
80×	`*-un-lft-identity_binary64`
58×	`add-cube-cbrt_binary64`
56×	`sqrt-prod_binary64`

Counts

3 → 168

Calls

3 calls:

20.0ms

(*.f64 (/.f64 (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b) b)) 2) (/.f64 (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b) b)) a))

5.0ms

(/.f64 (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b) b)) a)

3.0ms

(-.f64 (hypot.f64 (sqrt.f64 (*.f64 c (*.f64 a -4))) b) b)

simplify207.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

626×	`fma-def_binary64`
323×	`fma-neg_binary64`
314×	`cancel-sign-sub-inv_binary64`
215×	`neg-mul-1_binary64`
195×	`associate-*r/_binary64`

Counts

196 → 293

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	344	7621
1	877	6852
2	2826	6588
3	4458	6392
4	4931	6392
5	4901	6392

prune324.0ms (4.8%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	396	0	396
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	396	10	406

Error

2.4b

Counts

406 → 10

Alt Table

Status	Error	Program
	49.3b	(/.f64 (-.f64 b (hypot.f64 (.f64 (sqrt.f64 c) (sqrt.f64 (.f64 a -4))) b)) (*.f64 a -2))
✓	35.0b	(.f64 (/.f64 (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b) b)) 2) (/.f64 (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (*.f64 a -4))) b) b)) a))
	41.6b	(/.f64 (+.f64 (neg.f64 b) (exp.f64 (log.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b)))) (*.f64 2 a))
	55.2b	(/.f64 (+.f64 (neg.f64 b) b) (*.f64 2 a))
✓	34.9b	(/.f64 (-.f64 b (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b)) (*.f64 a -2))
	45.0b	(/.f64 (neg.f64 b) a)
▶	36.3b	(neg.f64 (/.f64 c b))
	49.6b	(cbrt.f64 (pow.f64 (/.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b) b) (*.f64 a 2)) 3))
	37.3b	(/.f64 (/.f64 (.f64 4 (.f64 c a)) (-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b))) (*.f64 2 a))
	38.3b	(/.f64 1 (/.f64 (.f64 2 a) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))))))

Compiler

Compiled 16278 to 10572 computations (35.1% saved)

localize3.0ms (0%)

prune6.0ms (0.1%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Kept	Total
New	0	0
Fresh	7	7
Picked	1	1
Done	2	2
Total	10	10

Error

2.4b

Counts

10 → 10

Alt Table

Status	Error	Program
	49.3b	(/.f64 (-.f64 b (hypot.f64 (.f64 (sqrt.f64 c) (sqrt.f64 (.f64 a -4))) b)) (*.f64 a -2))
✓	35.0b	(.f64 (/.f64 (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b) b)) 2) (/.f64 (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (*.f64 a -4))) b) b)) a))
	41.6b	(/.f64 (+.f64 (neg.f64 b) (exp.f64 (log.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b)))) (*.f64 2 a))
	55.2b	(/.f64 (+.f64 (neg.f64 b) b) (*.f64 2 a))
✓	34.9b	(/.f64 (-.f64 b (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b)) (*.f64 a -2))
	45.0b	(/.f64 (neg.f64 b) a)
✓	36.3b	(neg.f64 (/.f64 c b))
	49.6b	(cbrt.f64 (pow.f64 (/.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b) b) (*.f64 a 2)) 3))
	37.3b	(/.f64 (/.f64 (.f64 4 (.f64 c a)) (-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b))) (*.f64 2 a))
	38.3b	(/.f64 1 (/.f64 (.f64 2 a) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))))))

Compiler

Compiled 176 to 127 computations (27.8% saved)

regimes1.1s (16.5%)

Accuracy

Total 7.1b remaining (72.2%)

Threshold costs 0b (0%)

Counts

62 → 3

Compiler

Compiled 5535 to 3879 computations (29.9% saved)

bsearch77.0ms (1.2%)

Steps

Iters	Range		Point
10	4.241946271543068e-138	4.350640292110055e-126	4.1779810674765516e-126
9	-1.1141153340912374e+99	-1.146861339112528e+94	-1.0963394235440253e+99

Compiler

Compiled 4 to 3 computations (25% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	25	52
1	38	50
2	49	50
3	55	50
4	57	50
5	57	50

end136.0ms (2%)

Compiler: Compiled 250 to 171 computations (31.6% saved)

Details

analyze642.0ms (9.6%)

sample2.3s (35%)

simplify396.0ms (5.9%)

prune4.0ms (0.1%)

localize11.0ms (0.2%)

series129.0ms (1.9%)

rewrite25.0ms (0.4%)

simplify122.0ms (1.8%)

prune146.0ms (2.2%)

localize9.0ms (0.1%)

series260.0ms (3.9%)

rewrite15.0ms (0.2%)

simplify71.0ms (1.1%)

prune117.0ms (1.7%)

localize11.0ms (0.2%)

series495.0ms (7.4%)

rewrite51.0ms (0.8%)

simplify207.0ms (3.1%)

prune324.0ms (4.8%)

localize3.0ms (0%)

prune6.0ms (0.1%)

regimes1.1s (16.5%)

bsearch77.0ms (1.2%)

simplify3.0ms (0%)

end136.0ms (2%)

Profiling