Details

analyze774.0ms (7.8%)

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)

sample3.9s (39.8%)

Results

1.6s	1193×	body	2048	valid
1.1s	5399×	body	128	valid
393.0ms	743×	body	1024	valid
304.0ms	401×	body	4096	valid
209.0ms	1145×	body	128	invalid
160.0ms	370×	body	512	valid
37.0ms	150×	body	256	valid

Compiler

Compiled 62 to 44 computations (29% saved)

simplify262.0ms (2.6%)

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

33.9b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	34.0b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))
	34.0b	(.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)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (.f64 4 a) c)
✓	0.5b	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
✓	0.8b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
✓	22.2b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series101.0ms (1%)

Counts

4 → 100

Calls

4 calls:

51.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
31.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
11.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
7.0ms	(.f64 (.f64 4 a) c)

rewrite134.0ms (1.4%)

Algorithm

2×	batch-egg-rewrite

Rules

704×	`fma-def_binary64`
453×	`fma-neg_binary64`
270×	`egg-rr`
223×	`expm1-udef_binary64`
223×	`log1p-udef_binary64`

Counts

4 → 270

Calls

4 calls:

125.0ms	(.f64 (.f64 4 a) c)
125.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
125.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
125.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	55
1	271	47
2	3247	47
3	4973	47
4	4934	47
0	0	0
1	0	0

simplify78.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

458×	`times-frac_binary64`
447×	`unswap-sqr_binary64`
283×	`associate-r_binary64`
278×	`associate-/l*_binary64`
270×	`fma-def_binary64`

Counts

370 → 321

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	84	1797
1	270	1723
2	844	1661
3	4217	1661
4	5046	1661

prune335.0ms (3.4%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	311	10	321
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	312	11	323

Error

11.7b

Counts

323 → 11

Alt Table

Status	Error	Program
	46.1b	(/.f64 (fma.f64 b 1 (sqrt.f64 (fma.f64 -4 (.f64 a c) (.f64 b b)))) (*.f64 2 a))
	36.5b	(/.f64 (+.f64 (neg.f64 b) (pow.f64 (cbrt.f64 (sqrt.f64 (fma.f64 -4 (.f64 a c) (.f64 b b)))) 3)) (*.f64 2 a))
	36.0b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (fma.f64 (pow.f64 (cbrt.f64 b) 2) (.f64 (cbrt.f64 b) b) (.f64 -4 (.f64 a c))))) (.f64 2 a))
	44.6b	(/.f64 (-.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b) (*.f64 2 a))
	46.6b	(/.f64 (/.f64 (+.f64 (fma.f64 b b (.f64 b b)) (.f64 (.f64 4 a) c)) (-.f64 b (sqrt.f64 (fma.f64 -4 (.f64 a c) (.f64 b b))))) (.f64 2 a))
	46.6b	(/.f64 (.f64 (+.f64 (fma.f64 b b (.f64 b b)) (.f64 (.f64 4 a) c)) (/.f64 1 (-.f64 b (sqrt.f64 (fma.f64 -4 (.f64 a c) (.f64 b b)))))) (*.f64 2 a))
	47.2b	(/.f64 (.f64 -2 b) (.f64 2 a))
	47.9b	(/.f64 (.f64 -2 (fma.f64 (/.f64 c b) a (/.f64 (.f64 (.f64 c a) (.f64 c a)) (pow.f64 b 3)))) (*.f64 2 a))
	44.4b	(/.f64 (.f64 -2 (/.f64 (.f64 c a) b)) (*.f64 2 a))
▶	34.0b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
	56.0b	(/.f64 (+.f64 (neg.f64 b) b) (*.f64 2 a))

Compiler

Compiled 9918 to 5410 computations (45.5% saved)

localize10.0ms (0.1%)

Local error

Found 4 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))
✓	0.2b	(fma.f64 a (.f64 c -4) (.f64 b b))
✓	0.5b	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)
✓	22.2b	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))

series166.0ms (1.7%)

Counts

4 → 96

Calls

4 calls:

78.0ms	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
43.0ms	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)
33.0ms	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))
13.0ms	(fma.f64 a (.f64 c -4) (.f64 b b))

rewrite89.0ms (0.9%)

Algorithm

2×	batch-egg-rewrite

Rules

781×	`prod-diff_binary64`
244×	`log1p-udef_binary64`
165×	`egg-rr`
138×	`add-sqr-sqrt_binary64`
132×	`log1p-expm1-u_binary64`

Counts

4 → 165

Calls

4 calls:

85.0ms	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
85.0ms	(fma.f64 a (.f64 c -4) (.f64 b b))
85.0ms	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)
85.0ms	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	62
1	279	62
2	3385	62
3	5102	62
0	0	0
1	0	0

simplify89.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

742×	`times-frac_binary64`
467×	`associate-/l*_binary64`
436×	`fma-def_binary64`
432×	`fma-neg_binary64`
426×	`associate-/r*_binary64`

Counts

261 → 238

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	121	2241
1	398	2164
2	1327	2078
3	4954	2078
4	5218	2078

prune201.0ms (2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	231	7	238
Fresh	8	2	10
Picked	1	0	1
Done	0	0	0
Total	240	9	249

Error

7.2b

Counts

249 → 9

Alt Table

Status	Error	Program
	56.0b	(pow.f64 (pow.f64 (.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a)) 3) 1/3)
	35.3b	(.f64 (-.f64 (.f64 (cbrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) (cbrt.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))) b) (/.f64 1/2 a))
▶	34.0b	(/.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b) (*.f64 a 2))
	39.2b	(neg.f64 (/.f64 c b))
	46.6b	(/.f64 (/.f64 (+.f64 (fma.f64 b b (.f64 b b)) (.f64 (.f64 4 a) c)) (-.f64 b (sqrt.f64 (fma.f64 -4 (.f64 a c) (.f64 b b))))) (.f64 2 a))
	47.2b	(/.f64 (.f64 -2 b) (.f64 2 a))
	36.5b	(.f64 (-.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)))) 3) b) (/.f64 1/2 a))
	47.7b	(-.f64 (/.f64 c b) (/.f64 b a))
	43.4b	(/.f64 (.f64 (-.f64 (fma.f64 a (.f64 c -4) (.f64 b b)) (.f64 b b)) (/.f64 1/2 a)) (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))))

Compiler

Compiled 6480 to 3775 computations (41.7% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b) (*.f64 a 2))
	0.2b	(fma.f64 a (.f64 c -4) (.f64 b b))
	0.5b	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)
	22.2b	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))

series64.0ms (0.7%)

Counts

1 → 20

Calls

1 calls:

64.0ms

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

rewrite67.0ms (0.7%)

Algorithm

2×	batch-egg-rewrite

Rules

384×	`fma-def_binary64`
249×	`expm1-udef_binary64`
249×	`log1p-udef_binary64`
205×	`fma-neg_binary64`
140×	`add-sqr-sqrt_binary64`

Counts

1 → 60

Calls

1 calls:

65.0ms

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	22
1	281	22
2	3641	22
3	4875	22
0	0	0
1	0	0

simplify63.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

794×	`fma-neg_binary64`
351×	`unswap-sqr_binary64`
333×	`distribute-neg-frac_binary64`
328×	`times-frac_binary64`
221×	`associate-r_binary64`

Counts

80 → 83

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	64	612
1	210	609
2	666	585
3	3266	585
4	4979	585
5	5005	585

prune303.0ms (3.1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	255	1	256
Fresh	1	7	8
Picked	0	1	1
Done	0	0	0
Total	256	9	265

Error

7.2b

Counts

265 → 9

Alt Table

Status	Error	Program
	56.0b	(pow.f64 (pow.f64 (.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a)) 3) 1/3)
▶	35.3b	(.f64 (-.f64 (.f64 (cbrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) (cbrt.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))) b) (/.f64 1/2 a))
✓	34.0b	(/.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b) (*.f64 a 2))
	39.2b	(neg.f64 (/.f64 c b))
	46.6b	(/.f64 (/.f64 (+.f64 (fma.f64 b b (.f64 b b)) (.f64 (.f64 4 a) c)) (-.f64 b (sqrt.f64 (fma.f64 -4 (.f64 a c) (.f64 b b))))) (.f64 2 a))
	36.5b	(/.f64 (-.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) 3) b) (*.f64 a 2))
	47.2b	(/.f64 (.f64 -2 b) (.f64 2 a))
	47.7b	(-.f64 (/.f64 c b) (/.f64 b a))
	43.4b	(/.f64 (.f64 (-.f64 (fma.f64 a (.f64 c -4) (.f64 b b)) (.f64 b b)) (/.f64 1/2 a)) (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))))

Compiler

Compiled 6954 to 4117 computations (40.8% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(cbrt.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))
✓	7.1b	(-.f64 (.f64 (cbrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) (cbrt.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))))) b)
	22.2b	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))
✓	23.0b	(cbrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))

series174.0ms (1.8%)

Counts

3 → 92

Calls

3 calls:

84.0ms

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

51.0ms

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

39.0ms

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

rewrite79.0ms (0.8%)

Algorithm

2×	batch-egg-rewrite

Rules

904×	`prod-diff_binary64`
206×	`expm1-udef_binary64`
206×	`log1p-udef_binary64`
147×	`egg-rr`
120×	`add-sqr-sqrt_binary64`

Counts

3 → 147

Calls

3 calls:

75.0ms

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

75.0ms

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

75.0ms

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	44
1	248	43
2	2800	43
3	4928	43
0	0	0
1	0	0

simplify114.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

299×	`associate-r_binary64`
259×	`associate-/r*_binary64`
250×	`times-frac_binary64`
242×	`fma-neg_binary64`
206×	`fma-def_binary64`

Counts

239 → 274

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	365	4666
1	1221	4570
2	4688	4530
3	4966	4530

prune296.0ms (3%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	317	2	319
Fresh	2	5	7
Picked	0	1	1
Done	0	1	1
Total	319	9	328

Error

7.1b

Counts

328 → 9

Alt Table

Status	Error	Program
✓	34.0b	(/.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b) (*.f64 a 2))
	39.2b	(neg.f64 (/.f64 c b))
	46.6b	(/.f64 (/.f64 (+.f64 (fma.f64 b b (.f64 b b)) (.f64 (.f64 4 a) c)) (-.f64 b (sqrt.f64 (fma.f64 -4 (.f64 a c) (.f64 b b))))) (.f64 2 a))
	56.4b	(.f64 (-.f64 (.f64 (exp.f64 (.f64 1/3 (-.f64 (log.f64 (.f64 4 a)) (log.f64 (/.f64 -1 c))))) (cbrt.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))) b) (/.f64 1/2 a))
	54.2b	(.f64 (-.f64 (.f64 (exp.f64 (.f64 1/3 (-.f64 (log.f64 (.f64 4 c)) (log.f64 (/.f64 -1 a))))) (cbrt.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))) b) (/.f64 1/2 a))
	47.2b	(/.f64 (.f64 -2 b) (.f64 2 a))
✓	35.3b	(.f64 (-.f64 (.f64 (cbrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) (cbrt.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))) b) (/.f64 1/2 a))
	47.7b	(-.f64 (/.f64 c b) (/.f64 b a))
	43.4b	(/.f64 (.f64 (-.f64 (fma.f64 a (.f64 c -4) (.f64 b b)) (.f64 b b)) (/.f64 1/2 a)) (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))))

Compiler

Compiled 13520 to 8388 computations (38% saved)

regimes2.2s (22.4%)

Accuracy

Total 4.5b remaining (43.5%)

Threshold costs 0b (0%)

Counts

147 → 3

Compiler

Compiled 13008 to 8954 computations (31.2% saved)

bsearch72.0ms (0.7%)

Steps

Iters	Range		Point
6	1.4855380049205776e-100	1.0213362282975204e-99	1.001210637958157e-99
8	-1.761622937979916e+128	-7.291574701407998e+119	-1.3104263752164671e+126

Compiler

Compiled 4 to 3 computations (25% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	46
1	37	46
2	46	46
3	52	46
4	54	46
5	54	46

end216.0ms (2.2%)

Compiler: Compiled 268 to 176 computations (34.3% saved)

Details

analyze774.0ms (7.8%)

sample3.9s (39.8%)

simplify262.0ms (2.6%)

prune4.0ms (0%)

localize15.0ms (0.2%)

series101.0ms (1%)

rewrite134.0ms (1.4%)

simplify78.0ms (0.8%)

prune335.0ms (3.4%)

localize10.0ms (0.1%)

series166.0ms (1.7%)

rewrite89.0ms (0.9%)

simplify89.0ms (0.9%)

prune201.0ms (2%)

localize12.0ms (0.1%)

series64.0ms (0.7%)

rewrite67.0ms (0.7%)

simplify63.0ms (0.6%)

prune303.0ms (3.1%)

localize15.0ms (0.2%)

series174.0ms (1.8%)

rewrite79.0ms (0.8%)

simplify114.0ms (1.2%)

prune296.0ms (3%)

regimes2.2s (22.4%)

bsearch72.0ms (0.7%)

simplify3.0ms (0%)

end216.0ms (2.2%)

Profiling