Details

analyze610.0ms (9.4%)

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)

sample2.6s (39.6%)

Results

889.0ms	1212×	body	2048	valid
692.0ms	5276×	body	128	valid
353.0ms	795×	body	1024	valid
254.0ms	423×	body	4096	valid
135.0ms	1082×	body	128	invalid
109.0ms	354×	body	512	valid
43.0ms	196×	body	256	valid

Compiler

Compiled 62 to 44 computations (29% saved)

simplify257.0ms (4%)

Algorithm

1×	egg-herbie

Rules

1743×	`fma-neg_binary64`
1393×	`fma-def_binary64`
800×	`div-sub_binary64`
619×	`times-frac_binary64`
473×	`associate-/r/_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	26
1	33	22
2	67	22
3	138	22
4	204	22
5	338	22
6	558	22
7	924	22
8	1388	22
9	1604	22
10	2375	22
11	2742	22
12	2533	22
13	2621	22
14	3171	22
15	3313	22
16	3873	22
17	3679	22
18	4029	22
19	4317	22
20	4485	22
21	4561	22
22	4805	22
23	4793	22
24	4797	22
25	4797	22
26	4948	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
	38.3b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
▶	38.2b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))

Compiler

Compiled 111 to 74 computations (33.3% saved)

localize10.0ms (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 (.f64 4 a) c)))) (.f64 2 a))
✓	0.4b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
✓	0.7b	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
✓	26.8b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series132.0ms (2%)

Counts

4 → 96

Calls

4 calls:

55.0ms	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))
34.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
33.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
10.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

rewrite29.0ms (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:

10.0ms	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))
7.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
3.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify120.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

701×	`fma-neg_binary64`
334×	`cancel-sign-sub-inv_binary64`
215×	`distribute-rgt-neg-in_binary64`
159×	`associate-r_binary64`
150×	`distribute-rgt-neg-out_binary64`

Counts

186 → 207

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	243	4208
1	695	3858
2	2512	3724
3	4694	3704
4	5031	3704

prune150.0ms (2.3%)

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)
	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 (.f64 4 a) c))))))
	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))

Compiler

Compiled 5721 to 3361 computations (41.3% 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)))

series281.0ms (4.3%)

Counts

3 → 24

Calls

3 calls:

168.0ms	(/.f64 (-.f64 b (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b)) (*.f64 a -2))
99.0ms	(-.f64 b (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b))
14.0ms	(sqrt.f64 (.f64 c (.f64 a -4)))

rewrite17.0ms (0.3%)

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))
4.0ms	(sqrt.f64 (.f64 c (.f64 a -4)))
3.0ms	(-.f64 b (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b))

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

prune122.0ms (1.9%)

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
▶	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)
	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 (.f64 4 a) c))))))
	49.3b	(/.f64 (-.f64 b (hypot.f64 (.f64 (sqrt.f64 c) (sqrt.f64 (.f64 a -4))) b)) (*.f64 a -2))
	36.3b	(neg.f64 (/.f64 c b))

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)))

series494.0ms (7.6%)

Counts

3 → 28

Calls

3 calls:

267.0ms

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

138.0ms

(*.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))

88.0ms

(-.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))

6.0ms

(/.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)

simplify208.0ms (3.2%)

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

prune342.0ms (5.3%)

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
✓	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)
	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 (.f64 4 a) c))))))
	49.3b	(/.f64 (-.f64 b (hypot.f64 (.f64 (sqrt.f64 c) (sqrt.f64 (.f64 a -4))) b)) (*.f64 a -2))
▶	36.3b	(neg.f64 (/.f64 c b))

Compiler

Compiled 16278 to 10572 computations (35.1% saved)

localize3.0ms (0%)

prune8.0ms (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
✓	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)
	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 (.f64 4 a) c))))))
	49.3b	(/.f64 (-.f64 b (hypot.f64 (.f64 (sqrt.f64 c) (sqrt.f64 (.f64 a -4))) b)) (*.f64 a -2))
✓	36.3b	(neg.f64 (/.f64 c b))

Compiler

Compiled 176 to 127 computations (27.8% saved)

regimes775.0ms (11.9%)

Accuracy

Total 7.1b remaining (72.1%)

Threshold costs 0b (0%)

Counts

62 → 3

Compiler

Compiled 5535 to 3913 computations (29.3% saved)

bsearch80.0ms (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)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

10×	`+-commutative_binary64`
10×	`*-commutative_binary64`
9×	`sub-neg_binary64`
7×	`neg-sub0_binary64`
7×	`neg-mul-1_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	26	54
1	45	52
2	70	52
3	82	52
4	88	52
5	89	52
6	88	52

end139.0ms (2.1%)

Compiler: Compiled 252 to 173 computations (31.3% saved)

Details

analyze610.0ms (9.4%)

sample2.6s (39.6%)

simplify257.0ms (4%)

prune4.0ms (0.1%)

localize10.0ms (0.2%)

series132.0ms (2%)

rewrite29.0ms (0.4%)

simplify120.0ms (1.8%)

prune150.0ms (2.3%)

localize9.0ms (0.1%)

series281.0ms (4.3%)

rewrite17.0ms (0.3%)

simplify71.0ms (1.1%)

prune122.0ms (1.9%)

localize11.0ms (0.2%)

series494.0ms (7.6%)

rewrite51.0ms (0.8%)

simplify208.0ms (3.2%)

prune342.0ms (5.3%)

localize3.0ms (0%)

prune8.0ms (0.1%)

regimes775.0ms (11.9%)

bsearch80.0ms (1.2%)

simplify4.0ms (0.1%)

end139.0ms (2.1%)

Profiling