Details

analyze860.0ms (9.5%)

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
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)

sample2.5s (27.8%)

Results

704.0ms	5363×	body	128	valid
615.0ms	1172×	body	2048	valid
407.0ms	437×	body	4096	valid
317.0ms	745×	body	1024	valid
227.0ms	1084×	body	128	invalid
109.0ms	346×	body	512	valid
50.0ms	193×	body	256	valid

Compiler

Compiled 62 to 44 computations (29% saved)

simplify269.0ms (3%)

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

35.4b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	35.5b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
	35.7b	(/.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)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 a (.f64 c -4) (.f64 b b))
✓	0.1b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
✓	0.8b	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)
✓	25.1b	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))

series174.0ms (1.9%)

Counts

4 → 96

Calls

4 calls:

76.0ms	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
50.0ms	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)
39.0ms	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))
9.0ms	(fma.f64 a (.f64 c -4) (.f64 b b))

rewrite80.0ms (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:

76.0ms	(fma.f64 a (.f64 c -4) (.f64 b b))
76.0ms	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
76.0ms	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)
76.0ms	(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

simplify119.0ms (1.3%)

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

prune206.0ms (2.3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	229	9	238
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	231	9	240

Error

4.3b

Counts

240 → 9

Alt Table

Status	Error	Program
	46.8b	(/.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)))))
	43.4b	(-.f64 (/.f64 c b) (/.f64 b a))
	49.7b	(/.f64 (-.f64 (fma.f64 a (.f64 c -4) (.f64 b b)) (.f64 b b)) (.f64 (.f64 a 2) (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))))))
	37.8b	(neg.f64 (/.f64 c b))
	43.3b	(/.f64 (neg.f64 b) a)
▶	35.4b	(/.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b) (*.f64 a 2))
	47.1b	(.f64 (.f64 -2 (fma.f64 (/.f64 c b) a (/.f64 (.f64 (.f64 c a) (*.f64 c a)) (pow.f64 b 3)))) (/.f64 1/2 a))
	35.9b	(.f64 (.f64 (cbrt.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)) (pow.f64 (cbrt.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)) 2)) (/.f64 1/2 a))
	45.1b	(.f64 (.f64 -2 (/.f64 (*.f64 c a) b)) (/.f64 1/2 a))

Compiler

Compiled 6476 to 3763 computations (41.9% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(fma.f64 a (.f64 c -4) (.f64 b b))
✓	0.1b	(/.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b) (*.f64 a 2))
	0.8b	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)
	25.1b	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))

series79.0ms (0.9%)

Counts

1 → 20

Calls

1 calls:

79.0ms

(/.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 (0.7%)

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

prune177.0ms (1.9%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	254	2	256
Fresh	2	6	8
Picked	0	1	1
Done	0	0	0
Total	256	9	265

Error

4.3b

Counts

265 → 9

Alt Table

Status	Error	Program
	46.8b	(/.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)))))
	43.4b	(-.f64 (/.f64 c b) (/.f64 b a))
	43.3b	(/.f64 (neg.f64 b) a)
	37.4b	(fma.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) (/.f64 1/2 a) (neg.f64 (/.f64 b (*.f64 a 2))))
	37.8b	(neg.f64 (/.f64 c b))
✓	35.4b	(/.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b) (*.f64 a 2))
	47.1b	(.f64 (.f64 -2 (fma.f64 (/.f64 c b) a (/.f64 (.f64 (.f64 c a) (*.f64 c a)) (pow.f64 b 3)))) (/.f64 1/2 a))
▶	36.8b	(/.f64 (-.f64 (.f64 (cbrt.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) (cbrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) b) (.f64 a 2))
	45.1b	(.f64 (.f64 -2 (/.f64 (*.f64 c a) b)) (/.f64 1/2 a))

Compiler

Compiled 6922 to 4093 computations (40.9% saved)

localize14.0ms (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))))
✓	8.9b	(-.f64 (.f64 (cbrt.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) (cbrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)))) b)
	25.1b	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))
✓	25.9b	(cbrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))

series154.0ms (1.7%)

Counts

3 → 92

Calls

3 calls:

53.0ms

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

52.0ms

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

48.0ms

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

rewrite72.0ms (0.8%)

Algorithm

2×	batch-egg-rewrite

Rules

865×	`prod-diff_binary64`
208×	`expm1-udef_binary64`
208×	`log1p-udef_binary64`
147×	`egg-rr`
124×	`log1p-expm1-u_binary64`

Counts

3 → 147

Calls

3 calls:

67.0ms

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

67.0ms

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

67.0ms

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	59
1	266	43
2	2817	43
3	4881	43
0	0	0
1	0	0

simplify110.0ms (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

prune266.0ms (2.9%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	318	1	319
Fresh	1	6	7
Picked	0	1	1
Done	0	1	1
Total	319	9	328

Error

4.3b

Counts

328 → 9

Alt Table

Status	Error	Program
	46.8b	(/.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)))))
	43.4b	(-.f64 (/.f64 c b) (/.f64 b a))
	47.9b	(/.f64 (.f64 -2 (+.f64 (/.f64 (.f64 c a) b) (/.f64 (.f64 (.f64 c a) (.f64 c a)) (pow.f64 b 3)))) (.f64 a 2))
▶	37.4b	(fma.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) (/.f64 1/2 a) (neg.f64 (/.f64 b (*.f64 a 2))))
	43.3b	(/.f64 (neg.f64 b) a)
	37.8b	(neg.f64 (/.f64 c b))
✓	35.4b	(/.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b) (*.f64 a 2))
✓	36.8b	(/.f64 (-.f64 (.f64 (cbrt.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) (cbrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) b) (.f64 a 2))
	45.1b	(.f64 (.f64 -2 (/.f64 (*.f64 c a) b)) (/.f64 1/2 a))

Compiler

Compiled 13601 to 8432 computations (38% saved)

localize13.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(fma.f64 a (.f64 c -4) (.f64 b b))
✓	23.3b	(fma.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) (/.f64 1/2 a) (neg.f64 (/.f64 b (*.f64 a 2))))
	25.1b	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))

series72.0ms (0.8%)

Counts

1 → 20

Calls

1 calls:

72.0ms

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

rewrite157.0ms (1.7%)

Algorithm

2×	batch-egg-rewrite

Rules

554×	`prod-diff_binary64`
399×	`egg-rr`
271×	`log1p-udef_binary64`
165×	`add-sqr-sqrt_binary64`
155×	`log1p-expm1-u_binary64`

Counts

1 → 399

Calls

1 calls:

137.0ms

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	28
1	338	26
2	3755	26
3	5115	26
0	0	0
1	0	0

simplify81.0ms (0.9%)

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

419 → 422

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

prune507.0ms (5.6%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	500	1	501
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	500	10	510

Error

4.3b

Counts

510 → 10

Alt Table

Status	Error	Program
	46.8b	(/.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)))))
	43.4b	(-.f64 (/.f64 c b) (/.f64 b a))
	49.5b	(+.f64 (fma.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) (/.f64 1/2 a) (.f64 b (/.f64 1/2 a))) (fma.f64 1 (.f64 b (/.f64 1/2 a)) (*.f64 b (/.f64 1/2 a))))
	47.9b	(/.f64 (.f64 -2 (+.f64 (/.f64 (.f64 c a) b) (/.f64 (.f64 (.f64 c a) (.f64 c a)) (pow.f64 b 3)))) (.f64 a 2))
✓	37.4b	(fma.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) (/.f64 1/2 a) (neg.f64 (/.f64 b (*.f64 a 2))))
	43.3b	(/.f64 (neg.f64 b) a)
	37.8b	(neg.f64 (/.f64 c b))
✓	35.4b	(/.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b) (*.f64 a 2))
✓	36.8b	(/.f64 (-.f64 (.f64 (cbrt.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) (cbrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) b) (.f64 a 2))
	45.1b	(.f64 (.f64 -2 (/.f64 (*.f64 c a) b)) (/.f64 1/2 a))

Compiler

Compiled 23735 to 15055 computations (36.6% saved)

regimes2.7s (29.6%)

Accuracy

Total 4.7b remaining (45.5%)

Threshold costs 0b (0%)

Counts

117 → 5

Compiler

Compiled 10004 to 6938 computations (30.6% saved)

bsearch148.0ms (1.6%)

Steps

Iters	Range		Point
8	1.2344334649195314e-55	1.322700660035437e-51	4.4233955990605117e-54
5	6.863344029837293e-72	1.4734283974003753e-71	1.3948090615163448e-71
8	2.6189808425900012e-111	1.3010807537774533e-107	1.2846674157042731e-107
9	-1.2695432231346224e+46	-1.731480671832066e+41	-1.251564096671974e+46

Compiler

Compiled 4 to 3 computations (25% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	115
1	56	115
2	73	115
3	84	115
4	89	115
5	89	115

end149.0ms (1.6%)

Compiler: Compiled 360 to 214 computations (40.6% saved)

Details

analyze860.0ms (9.5%)

sample2.5s (27.8%)

simplify269.0ms (3%)

prune4.0ms (0%)

localize9.0ms (0.1%)

series174.0ms (1.9%)

rewrite80.0ms (0.9%)

simplify119.0ms (1.3%)

prune206.0ms (2.3%)

localize9.0ms (0.1%)

series79.0ms (0.9%)

rewrite67.0ms (0.7%)

simplify63.0ms (0.7%)

prune177.0ms (1.9%)

localize14.0ms (0.2%)

series154.0ms (1.7%)

rewrite72.0ms (0.8%)

simplify110.0ms (1.2%)

prune266.0ms (2.9%)

localize13.0ms (0.1%)

series72.0ms (0.8%)

rewrite157.0ms (1.7%)

simplify81.0ms (0.9%)

prune507.0ms (5.6%)

regimes2.7s (29.6%)

bsearch148.0ms (1.6%)

simplify6.0ms (0.1%)

end149.0ms (1.6%)

Profiling