Details

analyze427.0ms (6.7%)

Algorithm

1×

Search

True	Other	False	Iter
0%	0%	100%	0
0%	0%	100%	1
0%	0%	100%	2
0%	0%	100%	3
0%	0%	100%	4
0%	0%	100%	5
0%	0%	100%	6
0%	0%	100%	7
0%	0%	100%	8
0%	0%	100%	9
0%	0%	100%	10
0%	0%	100%	11
0%	0%	100%	12
0%	0%	100%	13
0%	0%	100%	14

Compiler

Compiled 43 to 31 computations (27.9% saved)

sample50.0ms (0.8%)

Algorithm

1×

intervals

Results

14.0ms	94×	body	256	valid
10.0ms	162×	body	128	valid
10.0ms	290×	pre	128	true
2.0ms	34×	body	128	nan

Compiler

Compiled 66 to 48 computations (27.3% saved)

simplify263.0ms (4.1%)

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

44.7b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	44.7b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
	44.8b	(/.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	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))
✓	0.1b	(fma.f64 a (.f64 c -4) (.f64 b b))
✓	0.3b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
✓	38.5b	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)

series202.0ms (3.2%)

Counts

4 → 96

Calls

4 calls:

87.0ms	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
59.0ms	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)
45.0ms	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))
10.0ms	(fma.f64 a (.f64 c -4) (.f64 b b))

rewrite23.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

42×	`add-sqr-sqrt_binary64`
32×	`*-un-lft-identity_binary64`
28×	`add-cube-cbrt_binary64`
18×	`prod-diff_binary64`
17×	`sqrt-prod_binary64`

Counts

4 → 109

Calls

4 calls:

9.0ms	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
4.0ms	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)
1.0ms	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))
0.0ms	(fma.f64 a (.f64 c -4) (.f64 b b))

simplify191.0ms (3%)

Algorithm

1×	egg-herbie

Rules

527×	`fma-neg_binary64`
338×	`distribute-rgt-in_binary64`
273×	`cancel-sign-sub-inv_binary64`
155×	`associate-l_binary64`
153×	`associate-r_binary64`

Counts

205 → 226

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	267	5424
1	673	4468
2	2524	4293
3	4550	4293
4	4991	4293
5	4994	4293
6	4884	4293

prune157.0ms (2.5%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	220	6	226
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	222	6	228

Error

0.1b

Counts

228 → 6

Alt Table

Status	Error	Program
▶	0.4b	(/.f64 (.f64 (+.f64 (.f64 c (.f64 a -4)) 0) (/.f64 1/2 a)) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b))
	44.7b	(/.f64 (.f64 (-.f64 (.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) (.f64 b b)) (/.f64 1/2 a)) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b))
	44.8b	(/.f64 (.f64 (-.f64 (pow.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) 3) (pow.f64 b 3)) (/.f64 1/2 a)) (+.f64 (.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) (+.f64 (.f64 b b) (.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b))))
	44.7b	(/.f64 (.f64 (-.f64 (.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) (.f64 b b)) 1/2) (.f64 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b) a))
	3.0b	(neg.f64 (fma.f64 2 (/.f64 (.f64 (.f64 a a) (pow.f64 c 3)) (pow.f64 b 5)) (fma.f64 5 (/.f64 (.f64 (pow.f64 a 3) (pow.f64 c 4)) (pow.f64 b 7)) (+.f64 (/.f64 c b) (/.f64 (.f64 c (*.f64 c a)) (pow.f64 b 3))))))
	3.4b	(.f64 (neg.f64 (+.f64 (.f64 2 (/.f64 (.f64 c a) b)) (+.f64 (.f64 2 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b 3))) (+.f64 (.f64 10 (/.f64 (.f64 (pow.f64 c 4) (pow.f64 a 4)) (pow.f64 b 7))) (.f64 4 (/.f64 (*.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5))))))) (/.f64 1/2 a))

Compiler

Compiled 6417 to 3730 computations (41.9% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)
✓	0.1b	(/.f64 (.f64 (+.f64 (.f64 c (.f64 a -4)) 0) (/.f64 1/2 a)) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b))
	0.1b	(fma.f64 a (.f64 c -4) (.f64 b b))
✓	0.3b	(.f64 (+.f64 (.f64 c (*.f64 a -4)) 0) (/.f64 1/2 a))

series327.0ms (5.1%)

Counts

3 → 64

Calls

3 calls:

270.0ms

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

52.0ms

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

4.0ms

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

rewrite32.0ms (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:

13.0ms

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

9.0ms

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

3.0ms

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

simplify126.0ms (2%)

Algorithm

1×	egg-herbie

Rules

616×	`fma-neg_binary64`
248×	`associate-l_binary64`
225×	`associate-/l*_binary64`
220×	`associate-r_binary64`
176×	`div-sub_binary64`

Counts

156 → 198

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	250	3787
1	708	3244
2	3132	3157
3	4613	3157
4	4932	3157

prune214.0ms (3.4%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	211	6	217
Fresh	4	1	5
Picked	1	0	1
Done	0	0	0
Total	216	7	223

Error

Counts

223 → 7

Alt Table

Status	Error	Program
	0.5b	(.f64 (.f64 (+.f64 (.f64 c (.f64 a -4)) 0) (/.f64 1/2 a)) (/.f64 1 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)))
	0.7b	(/.f64 (.f64 (.f64 c (.f64 (.f64 a -4) (sqrt.f64 (/.f64 1/2 a)))) (sqrt.f64 (/.f64 1/2 a))) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b))
	3.0b	(neg.f64 (fma.f64 2 (/.f64 (.f64 (.f64 a a) (pow.f64 c 3)) (pow.f64 b 5)) (fma.f64 5 (/.f64 (.f64 (pow.f64 a 3) (pow.f64 c 4)) (pow.f64 b 7)) (+.f64 (/.f64 c b) (/.f64 (.f64 c (*.f64 c a)) (pow.f64 b 3))))))
	45.5b	(.f64 (/.f64 (.f64 (+.f64 (.f64 c (.f64 a -4)) 0) (/.f64 1/2 a)) (-.f64 (.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) (.f64 b b))) (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b))
	0.5b	(/.f64 (.f64 (+.f64 (.f64 c (.f64 a -4)) 0) 1/2) (.f64 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b) a))
	0.4b	(/.f64 (.f64 (+.f64 (.f64 c (.f64 a -4)) 0) (/.f64 1/2 a)) (fma.f64 (sqrt.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) (sqrt.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)))) b))
▶	0.1b	(/.f64 (.f64 -2 c) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b))

Compiler

Compiled 7300 to 4592 computations (37.1% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series274.0ms (4.3%)

Counts

1 → 20

Calls

1 calls:

274.0ms

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

rewrite9.0ms (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:

7.0ms

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

simplify63.0ms (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

prune152.0ms (2.4%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	178	4	182
Fresh	5	1	6
Picked	1	0	1
Done	0	0	0
Total	184	5	189

Error

Counts

189 → 5

Alt Table

Status	Error	Program
▶	0.2b	(/.f64 (.f64 -2 c) (fma.f64 (sqrt.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) (sqrt.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)))) b))
	3.0b	(-.f64 (.f64 (/.f64 (.f64 (pow.f64 c 3) (.f64 a a)) (pow.f64 b 5)) -2) (fma.f64 5 (/.f64 (.f64 (pow.f64 c 4) (pow.f64 a 3)) (pow.f64 b 7)) (fma.f64 (/.f64 (*.f64 c c) (pow.f64 b 3)) a (/.f64 c b))))
	0.7b	(/.f64 (.f64 (.f64 c (.f64 (.f64 a -4) (sqrt.f64 (/.f64 1/2 a)))) (sqrt.f64 (/.f64 1/2 a))) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b))
	0.6b	(/.f64 (/.f64 (.f64 -2 c) (sqrt.f64 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b))) (sqrt.f64 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b)))
	0.3b	(.f64 (.f64 -2 c) (/.f64 1 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)))

Compiler

Compiled 4734 to 2848 computations (39.8% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series410.0ms (6.4%)

Counts

3 → 108

Calls

3 calls:

245.0ms

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

103.0ms

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

61.0ms

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

rewrite11.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`sqrt-prod_binary64`
9×	`add-sqr-sqrt_binary64`
8×	`add-cbrt-cube_binary64`
8×	`add-exp-log_binary64`
7×	`*-un-lft-identity_binary64`

Counts

3 → 54

Calls

3 calls:

3.0ms

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

1.0ms

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

0.0ms

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

simplify178.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

742×	`times-frac_binary64`
332×	`fma-def_binary64`
205×	`*-commutative_binary64`
174×	`fma-neg_binary64`
136×	`distribute-neg-in_binary64`

Counts

162 → 246

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	610	8925
1	2099	8542
2	4978	8534
3	5076	8534

prune420.0ms (6.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	360	0	360
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	360	5	365

Error

Counts

365 → 5

Alt Table

Status	Error	Program
✓	0.2b	(/.f64 (.f64 -2 c) (fma.f64 (sqrt.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) (sqrt.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)))) b))
	3.0b	(-.f64 (.f64 (/.f64 (.f64 (pow.f64 c 3) (.f64 a a)) (pow.f64 b 5)) -2) (fma.f64 5 (/.f64 (.f64 (pow.f64 c 4) (pow.f64 a 3)) (pow.f64 b 7)) (fma.f64 (/.f64 (*.f64 c c) (pow.f64 b 3)) a (/.f64 c b))))
	0.7b	(/.f64 (.f64 (.f64 c (.f64 (.f64 a -4) (sqrt.f64 (/.f64 1/2 a)))) (sqrt.f64 (/.f64 1/2 a))) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b))
	0.6b	(/.f64 (/.f64 (.f64 -2 c) (sqrt.f64 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b))) (sqrt.f64 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b)))
	0.3b	(.f64 (.f64 -2 c) (/.f64 1 (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)))

Compiler

Compiled 18107 to 12202 computations (32.6% saved)

regimes1.2s (18.7%)

Accuracy

Total 0.1b remaining (85.7%)

Threshold costs 0.1b (85.7%)

Counts

242 → 1

Compiler

Compiled 29072 to 19350 computations (33.4% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64`
1×	`+-commutative_binary64`
1×	`*-lft-identity_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	22
1	22	22
2	20	22

end1.0ms (0%)

Compiler: Compiled 18 to 12 computations (33.3% saved)

sample1.6s (25%)

Algorithm

1×

intervals

Results

373.0ms	2947×	body	256	valid
343.0ms	5051×	body	128	valid
318.0ms	8963×	pre	128	true
65.0ms	963×	body	128	nan
0.0ms	2×	body	512	valid

Compiler

Compiled 217 to 148 computations (31.8% saved)

Details

analyze427.0ms (6.7%)

sample50.0ms (0.8%)

simplify263.0ms (4.1%)

prune4.0ms (0.1%)

localize10.0ms (0.2%)

series202.0ms (3.2%)

rewrite23.0ms (0.4%)

simplify191.0ms (3%)

prune157.0ms (2.5%)

localize14.0ms (0.2%)

series327.0ms (5.1%)

rewrite32.0ms (0.5%)

simplify126.0ms (2%)

prune214.0ms (3.4%)

localize9.0ms (0.1%)

series274.0ms (4.3%)

rewrite9.0ms (0.1%)

simplify63.0ms (1%)

prune152.0ms (2.4%)

localize11.0ms (0.2%)

series410.0ms (6.4%)

rewrite11.0ms (0.2%)

simplify178.0ms (2.8%)

prune420.0ms (6.6%)

regimes1.2s (18.7%)

simplify2.0ms (0%)

end1.0ms (0%)

sample1.6s (25%)

Profiling