Details

analyze657.0ms (6.2%)

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)

sample2.7s (25.4%)

Results

933.0ms	5655×	body	128	valid
695.0ms	1093×	body	2048	valid
329.0ms	635×	body	1024	valid
287.0ms	373×	body	4096	valid
133.0ms	343×	body	512	valid
109.0ms	669×	body	128	invalid
44.0ms	157×	body	256	valid

Compiler

Compiled 62 to 44 computations (29% saved)

simplify301.0ms (2.8%)

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%)

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 (.f64 4 a) c)))) (.f64 2 a))

Compiler

Compiled 111 to 74 computations (33.3% saved)

localize12.0ms (0.1%)

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

series361.0ms (3.4%)

Counts

4 → 96

Calls

4 calls:

166.0ms	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))
107.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
66.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
21.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

rewrite59.0ms (0.6%)

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:

19.0ms	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))
14.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
7.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
7.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify231.0ms (2.2%)

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

prune357.0ms (3.4%)

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
	39.9b	(/.f64 (neg.f64 b) a)
	29.0b	(.f64 (/.f64 (sqrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) 2) (/.f64 (sqrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))) a))
	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))
	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))))
▶	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))

Compiler

Compiled 5699 to 3321 computations (41.7% saved)

localize21.0ms (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)))

series350.0ms (3.3%)

Counts

3 → 60

Calls

3 calls:

162.0ms	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
106.0ms	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)
82.0ms	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))

rewrite26.0ms (0.2%)

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:

9.0ms	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
6.0ms	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))
5.0ms	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)

simplify153.0ms (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

prune181.0ms (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
	39.9b	(/.f64 (neg.f64 b) a)
	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)))))))
	40.0b	(-.f64 (/.f64 c b) (/.f64 b 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))
	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))
✓	28.9b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))

Compiler

Compiled 5742 to 3336 computations (41.9% saved)

localize13.0ms (0.1%)

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)))

series354.0ms (3.3%)

Counts

3 → 64

Calls

3 calls:

296.0ms

(/.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))

55.0ms

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

3.0ms

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

rewrite32.0ms (0.3%)

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:

11.0ms

(/.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))

9.0ms

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

3.0ms

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

simplify152.0ms (1.4%)

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

prune184.0ms (1.7%)

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
▶	31.9b	(/.f64 (.f64 -2 c) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b))
	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))
✓	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)))
	40.0b	(-.f64 (/.f64 c b) (/.f64 b a))

Compiler

Compiled 7929 to 5001 computations (36.9% saved)

localize11.0ms (0.1%)

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)))

series286.0ms (2.7%)

Counts

1 → 20

Calls

1 calls:

285.0ms

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

rewrite8.0ms (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:

6.0ms

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

simplify68.0ms (0.6%)

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

prune118.0ms (1.1%)

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
	37.3b	(/.f64 (.f64 -2 c) (+.f64 (exp.f64 (log.f64 (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -4)))))) 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))
✓	31.9b	(/.f64 (.f64 -2 c) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b))
	41.5b	(neg.f64 (/.f64 c b))
	32.5b	(/.f64 -2 (/.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4))))) c))
✓	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))

Compiler

Compiled 4171 to 2512 computations (39.8% saved)

regimes3.8s (35.6%)

Accuracy

Total 1.0b remaining (16.7%)

Threshold costs 1.0b (16.7%)

Counts

187 → 4

Compiler

Compiled 16943 to 11895 computations (29.8% saved)

bsearch118.0ms (1.1%)

Steps

Iters	Range		Point
7	4.199021549675812e+120	7.979983627339533e+128	5.69311637248718e+122
7	4.199590604817195e-304	9.40127380898348e-302	5.206369630189784e-304
4	-4.8293727107314014e+85	-1.0473602901519483e+84	-3.765674528228214e+85

Compiler

Compiled 4 to 3 computations (25% saved)

simplify5.0ms (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: 0 (0.0ms)

Iter	Nodes	Cost
0	37	80
1	60	80
2	83	80
3	95	80
4	101	80
5	102	80
6	101	80

end105.0ms (1%)

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

Details

analyze657.0ms (6.2%)

sample2.7s (25.4%)

simplify301.0ms (2.8%)

prune4.0ms (0%)

localize12.0ms (0.1%)

series361.0ms (3.4%)

rewrite59.0ms (0.6%)

simplify231.0ms (2.2%)

prune357.0ms (3.4%)

localize21.0ms (0.2%)

series350.0ms (3.3%)

rewrite26.0ms (0.2%)

simplify153.0ms (1.4%)

prune181.0ms (1.7%)

localize13.0ms (0.1%)

series354.0ms (3.3%)

rewrite32.0ms (0.3%)

simplify152.0ms (1.4%)

prune184.0ms (1.7%)

localize11.0ms (0.1%)

series286.0ms (2.7%)

rewrite8.0ms (0.1%)

simplify68.0ms (0.6%)

prune118.0ms (1.1%)

regimes3.8s (35.6%)

bsearch118.0ms (1.1%)

simplify5.0ms (0%)

end105.0ms (1%)

Profiling