Details

analyze646.0ms (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
25%	74.9%	0.1%	4
37.4%	62.4%	0.1%	5
37.4%	62.4%	0.1%	6
37.4%	56.2%	6.4%	7
45.2%	48.4%	6.4%	8
49.1%	42.1%	8.7%	9
51.5%	35.1%	13.4%	10
58.1%	27.7%	14.2%	11
60.8%	22.6%	16.5%	12
62.3%	18.7%	19%	13
66.2%	14.4%	19.4%	14

Compiler

Compiled 21 to 15 computations (28.6% saved)

sample3.0s (23.1%)

Results

1.0s	5655×	body	128	valid
780.0ms	1093×	body	2048	valid
356.0ms	635×	body	1024	valid
306.0ms	373×	body	4096	valid
167.0ms	343×	body	512	valid
117.0ms	669×	body	128	invalid
46.0ms	157×	body	256	valid

Compiler

Compiled 62 to 44 computations (29% saved)

simplify654.0ms (5.1%)

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

prune8.0ms (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

28.8b

Counts

3 → 2

Alt Table

Status	Error	Program
	28.9b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
▶	28.9b	(/.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)

localize22.0ms (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))
✓	0.8b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
✓	1.0b	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
✓	25.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

series362.0ms (2.8%)

Counts

4 → 96

Calls

4 calls:

155.0ms	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (.f64 2 a))
98.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
91.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
18.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

rewrite55.0ms (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:

17.0ms	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (.f64 2 a))
13.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
6.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
6.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

simplify221.0ms (1.7%)

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

prune724.0ms (5.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	199	8	207
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	200	9	209

Error

3.5b

Counts

209 → 9

Alt Table

Status	Error	Program
	44.7b	(fma.f64 1/4 (/.f64 (.f64 b b) (.f64 a (sqrt.f64 (.f64 c (.f64 a -4))))) (.f64 1/2 (-.f64 (/.f64 (sqrt.f64 (.f64 c (*.f64 a -4))) a) (/.f64 b a))))
	29.6b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 (.f64 c a) -4 (.f64 b b))) (cbrt.f64 (fma.f64 (.f64 c a) -4 (.f64 b b)))) (cbrt.f64 (fma.f64 (.f64 c a) -4 (.f64 b b)))))) (*.f64 2 a))
	39.2b	(/.f64 (/.f64 (.f64 4 (.f64 c a)) (-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b))) (*.f64 2 a))
▶	28.9b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
	29.0b	(.f64 (/.f64 (sqrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))))) 2) (/.f64 (sqrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))) a))
	40.0b	(-.f64 (/.f64 c b) (/.f64 b a))
	39.9b	(/.f64 (neg.f64 b) a)
	41.5b	(neg.f64 (/.f64 c b))
	47.0b	(.f64 (sqrt.f64 (/.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b) b) (.f64 a 2))) (sqrt.f64 (/.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b) b) (*.f64 a 2))))

Compiler

Compiled 5699 to 3180 computations (44.2% saved)

localize22.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
✓	1.0b	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)
✓	25.0b	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))

series367.0ms (2.8%)

Counts

3 → 60

Calls

3 calls:

166.0ms	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
109.0ms	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)
91.0ms	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))

rewrite47.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

41×	`add-sqr-sqrt_binary64`
31×	`*-un-lft-identity_binary64`
27×	`add-cube-cbrt_binary64`
18×	`prod-diff_binary64`
17×	`sqrt-prod_binary64`

Counts

3 → 99

Calls

3 calls:

18.0ms	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
9.0ms	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)
2.0ms	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))

simplify187.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

505×	`fma-neg_binary64`
316×	`distribute-rgt-in_binary64`
279×	`distribute-lft-in_binary64`
261×	`cancel-sign-sub-inv_binary64`
151×	`associate-r_binary64`

Counts

159 → 207

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	258	4859
1	662	3980
2	2479	3807
3	4859	3807
4	4966	3807

prune223.0ms (1.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	205	2	207
Fresh	4	4	8
Picked	0	1	1
Done	0	0	0
Total	209	7	216

Error

3.5b

Counts

216 → 7

Alt Table

Status	Error	Program
	38.4b	(/.f64 (.f64 1/2 (+.f64 (.f64 a (.f64 c -4)) 0)) (.f64 a (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))))
	41.5b	(neg.f64 (/.f64 c b))
✓	28.9b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
	40.0b	(-.f64 (/.f64 c b) (/.f64 b a))
	39.9b	(/.f64 (neg.f64 b) a)
	39.2b	(/.f64 (/.f64 (.f64 4 (.f64 c a)) (-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b))) (*.f64 2 a))
▶	33.4b	(/.f64 (.f64 (+.f64 (.f64 a (.f64 c -4)) 0) (/.f64 1/2 a)) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b))

Compiler

Compiled 5742 to 3336 computations (41.9% saved)

localize27.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (.f64 (+.f64 (.f64 a (.f64 c -4)) 0) (/.f64 1/2 a)) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b))
✓	0.6b	(+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)
✓	11.0b	(.f64 (+.f64 (.f64 a (*.f64 c -4)) 0) (/.f64 1/2 a))
	25.0b	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))

series520.0ms (4%)

Counts

3 → 64

Calls

3 calls:

440.0ms

(/.f64 (*.f64 (+.f64 (*.f64 a (*.f64 c -4)) 0) (/.f64 1/2 a)) (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b))

73.0ms

(+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b)

6.0ms

(*.f64 (+.f64 (*.f64 a (*.f64 c -4)) 0) (/.f64 1/2 a))

rewrite66.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`*-un-lft-identity_binary64`
20×	`add-sqr-sqrt_binary64`
17×	`add-cbrt-cube_binary64`
17×	`add-exp-log_binary64`
15×	`add-cube-cbrt_binary64`

Counts

3 → 92

Calls

3 calls:

26.0ms

(/.f64 (*.f64 (+.f64 (*.f64 a (*.f64 c -4)) 0) (/.f64 1/2 a)) (+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b))

20.0ms

(*.f64 (+.f64 (*.f64 a (*.f64 c -4)) 0) (/.f64 1/2 a))

7.0ms

(+.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))) b)

simplify264.0ms (2%)

Algorithm

1×	egg-herbie

Rules

645×	`fma-neg_binary64`
245×	`associate-l_binary64`
225×	`associate-/l*_binary64`
221×	`associate-r_binary64`
177×	`div-sub_binary64`

Counts

156 → 196

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	249	3787
1	704	3238
2	3118	3153
3	4528	3153
4	4998	3153
5	4903	3153

prune376.0ms (2.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	238	2	240
Fresh	2	3	5
Picked	1	0	1
Done	0	1	1
Total	241	6	247

Error

3.5b

Counts

247 → 6

Alt Table

Status	Error	Program
	40.0b	(-.f64 (/.f64 c b) (/.f64 b a))
▶	31.9b	(/.f64 (.f64 -2 c) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b))
✓	28.9b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
	34.9b	(/.f64 1 (/.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 c (.f64 a -4))))) (/.f64 (.f64 (.f64 c a) -2) a)))
	41.5b	(neg.f64 (/.f64 c b))
	39.2b	(/.f64 (/.f64 (.f64 4 (.f64 c a)) (-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b))) (*.f64 2 a))

Compiler

Compiled 7929 to 5001 computations (36.9% saved)

localize21.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (.f64 -2 c) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b))
	0.6b	(+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)
	25.0b	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))

series498.0ms (3.8%)

Counts

1 → 20

Calls

1 calls:

498.0ms

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

rewrite13.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`*-un-lft-identity_binary64`
6×	`add-cbrt-cube_binary64`
6×	`add-exp-log_binary64`
4×	`associate-/r*_binary64`
4×	`times-frac_binary64`

Counts

1 → 27

Calls

1 calls:

10.0ms

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

simplify141.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

769×	`times-frac_binary64`
615×	`associate-/l*_binary64`
357×	`associate-/r*_binary64`
352×	`fma-neg_binary64`
235×	`fma-def_binary64`

Counts

47 → 67

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	127	1488
1	366	1333
2	1180	1254
3	4844	1254
4	5078	1254

prune240.0ms (1.9%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	159	2	161
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	160	7	167

Error

3.5b

Counts

167 → 7

Alt Table

Status	Error	Program
	40.0b	(-.f64 (/.f64 c b) (/.f64 b a))
✓	31.9b	(/.f64 (.f64 -2 c) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b))
✓	28.9b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
	41.5b	(neg.f64 (/.f64 c b))
	39.2b	(/.f64 (/.f64 (.f64 4 (.f64 c a)) (-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b))) (*.f64 2 a))
	37.3b	(/.f64 (.f64 -2 c) (+.f64 (exp.f64 (log.f64 (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -4)))))) b))
	32.5b	(/.f64 -2 (/.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4))))) c))

Compiler

Compiled 4171 to 2512 computations (39.8% saved)

regimes4.0s (30.8%)

Accuracy

Total 1.0b remaining (16.7%)

Threshold costs 1.0b (16.7%)

Counts

187 → 4

Compiler

Compiled 16943 to 11828 computations (30.2% saved)

bsearch104.0ms (0.8%)

Steps

Iters	Range		Point
7	4.199021549675812e+120	7.979983627339533e+128	5.69311637248718e+122
7	4.199590604817195e-304	9.40127380898348e-302	4.311454940969704e-304
4	-4.8293727107314014e+85	-1.0473602901519483e+84	-3.765674528228214e+85

Compiler

Compiled 4 to 3 computations (25% saved)

simplify6.0ms (0%)

Algorithm

1×	egg-herbie

Rules

12×	`*-commutative_binary64`
11×	`+-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	39	82
1	62	80
2	79	80
3	94	80
4	101	80
5	104	80
6	105	80
7	103	80

end157.0ms (1.2%)

Compiler: Compiled 227 to 146 computations (35.7% saved)

Details

analyze646.0ms (5%)

sample3.0s (23.1%)

simplify654.0ms (5.1%)

prune8.0ms (0.1%)

localize22.0ms (0.2%)

series362.0ms (2.8%)

rewrite55.0ms (0.4%)

simplify221.0ms (1.7%)

prune724.0ms (5.6%)

localize22.0ms (0.2%)

series367.0ms (2.8%)

rewrite47.0ms (0.4%)

simplify187.0ms (1.4%)

prune223.0ms (1.7%)

localize27.0ms (0.2%)

series520.0ms (4%)

rewrite66.0ms (0.5%)

simplify264.0ms (2%)

prune376.0ms (2.9%)

localize21.0ms (0.2%)

series498.0ms (3.8%)

rewrite13.0ms (0.1%)

simplify141.0ms (1.1%)

prune240.0ms (1.9%)

regimes4.0s (30.8%)

bsearch104.0ms (0.8%)

simplify6.0ms (0%)

end157.0ms (1.2%)

Profiling