Details

analyze618.0ms (11.8%)

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)

sample2.9s (54.8%)

Results

968.0ms	1212×	body	2048	valid
803.0ms	5276×	body	128	valid
432.0ms	795×	body	1024	valid
284.0ms	423×	body	4096	valid
136.0ms	1082×	body	128	invalid
119.0ms	354×	body	512	valid
43.0ms	196×	body	256	valid

Compiler

Compiled 62 to 44 computations (29% saved)

simplify256.0ms (4.9%)

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

prune3.0ms (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

38.2b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	38.2b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))
	38.3b	(.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)

localize10.0ms (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 (.f64 4 a) c)))) (.f64 2 a))
✓	0.4b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
✓	0.7b	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
✓	26.8b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series126.0ms (2.4%)

Counts

4 → 96

Calls

4 calls:

54.0ms	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))
34.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
29.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
9.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

rewrite131.0ms (2.5%)

Algorithm

1×	batch-egg-rewrite

Rules

278×	`expm1-udef_binary64`
278×	`log1p-udef_binary64`
166×	`add-sqr-sqrt_binary64`
162×	`log1p-expm1-u_binary64`
162×	`expm1-log1p-u_binary64`

Counts

4 → 158

Calls

4 calls:

127.0ms	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))
127.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
127.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
127.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	74
1	337	62
2	4158	62
3	4987	62
4	4850	62

simplify78.0ms (1.5%)

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

254 → 231

Iterations

Useful iterations: 2 (0.0ms)

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

prune162.0ms (3.1%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	222	9	231
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	223	10	233

Error

4.9b

Counts

233 → 10

Alt Table

Status	Error	Program
	45.2b	(-.f64 (/.f64 c b) (/.f64 b a))
	45.0b	(/.f64 (neg.f64 b) a)
▶	36.3b	(neg.f64 (/.f64 c b))
	49.7b	(/.f64 (/.f64 (-.f64 (.f64 b b) (fma.f64 b b (.f64 -4 (.f64 a c)))) (-.f64 b (sqrt.f64 (fma.f64 b b (.f64 -4 (.f64 a c)))))) (.f64 2 a))
	55.2b	(/.f64 (+.f64 (neg.f64 b) b) (*.f64 2 a))
✓	38.2b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))
	57.2b	(cbrt.f64 (pow.f64 (.f64 (+.f64 b (sqrt.f64 (fma.f64 b b (.f64 -4 (*.f64 a c))))) (/.f64 1/2 a)) 3))
	49.4b	(pow.f64 (/.f64 (.f64 a 2) (+.f64 b (sqrt.f64 (fma.f64 b b (.f64 -4 (*.f64 a c)))))) -1)
	49.6b	(pow.f64 (cbrt.f64 (.f64 (+.f64 b (sqrt.f64 (fma.f64 b b (.f64 -4 (*.f64 a c))))) (/.f64 1/2 a))) 3)
	49.4b	(.f64 (/.f64 (sqrt.f64 (+.f64 b (sqrt.f64 (fma.f64 b b (.f64 -4 (.f64 a c)))))) a) (/.f64 (sqrt.f64 (+.f64 b (sqrt.f64 (fma.f64 b b (.f64 -4 (*.f64 a c)))))) 2))

Compiler

Compiled 6072 to 3568 computations (41.2% saved)

localize3.0ms (0.1%)

prune10.0ms (0.2%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Kept	Total
New	0	0
Fresh	8	8
Picked	1	1
Done	1	1
Total	10	10

Error

4.9b

Counts

10 → 10

Alt Table

Status	Error	Program
	45.2b	(-.f64 (/.f64 c b) (/.f64 b a))
▶	45.0b	(/.f64 (neg.f64 b) a)
✓	36.3b	(neg.f64 (/.f64 c b))
	49.7b	(/.f64 (/.f64 (-.f64 (.f64 b b) (fma.f64 b b (.f64 -4 (.f64 a c)))) (-.f64 b (sqrt.f64 (fma.f64 b b (.f64 -4 (.f64 a c)))))) (.f64 2 a))
	55.2b	(/.f64 (+.f64 (neg.f64 b) b) (*.f64 2 a))
✓	38.2b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))
	57.2b	(cbrt.f64 (pow.f64 (.f64 (+.f64 b (sqrt.f64 (fma.f64 b b (.f64 -4 (*.f64 a c))))) (/.f64 1/2 a)) 3))
	49.4b	(pow.f64 (/.f64 (.f64 a 2) (+.f64 b (sqrt.f64 (fma.f64 b b (.f64 -4 (*.f64 a c)))))) -1)
	49.6b	(pow.f64 (cbrt.f64 (.f64 (+.f64 b (sqrt.f64 (fma.f64 b b (.f64 -4 (*.f64 a c))))) (/.f64 1/2 a))) 3)
	49.4b	(.f64 (/.f64 (sqrt.f64 (+.f64 b (sqrt.f64 (fma.f64 b b (.f64 -4 (.f64 a c)))))) a) (/.f64 (sqrt.f64 (+.f64 b (sqrt.f64 (fma.f64 b b (.f64 -4 (*.f64 a c)))))) 2))

Compiler

Compiled 333 to 221 computations (33.6% saved)

localize3.0ms (0.1%)

prune9.0ms (0.2%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Kept	Total
New	0	0
Fresh	7	7
Picked	1	1
Done	2	2
Total	10	10

Error

4.9b

Counts

10 → 10

Alt Table

Status	Error	Program
▶	45.2b	(-.f64 (/.f64 c b) (/.f64 b a))
✓	45.0b	(/.f64 (neg.f64 b) a)
✓	36.3b	(neg.f64 (/.f64 c b))
	49.7b	(/.f64 (/.f64 (-.f64 (.f64 b b) (fma.f64 b b (.f64 -4 (.f64 a c)))) (-.f64 b (sqrt.f64 (fma.f64 b b (.f64 -4 (.f64 a c)))))) (.f64 2 a))
	55.2b	(/.f64 (+.f64 (neg.f64 b) b) (*.f64 2 a))
✓	38.2b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))
	57.2b	(cbrt.f64 (pow.f64 (.f64 (+.f64 b (sqrt.f64 (fma.f64 b b (.f64 -4 (*.f64 a c))))) (/.f64 1/2 a)) 3))
	49.4b	(pow.f64 (/.f64 (.f64 a 2) (+.f64 b (sqrt.f64 (fma.f64 b b (.f64 -4 (*.f64 a c)))))) -1)
	49.6b	(pow.f64 (cbrt.f64 (.f64 (+.f64 b (sqrt.f64 (fma.f64 b b (.f64 -4 (*.f64 a c))))) (/.f64 1/2 a))) 3)
	49.4b	(.f64 (/.f64 (sqrt.f64 (+.f64 b (sqrt.f64 (fma.f64 b b (.f64 -4 (.f64 a c)))))) a) (/.f64 (sqrt.f64 (+.f64 b (sqrt.f64 (fma.f64 b b (.f64 -4 (*.f64 a c)))))) 2))

Compiler

Compiled 326 to 216 computations (33.7% saved)

localize4.0ms (0.1%)

prune6.0ms (0.1%)

Pruning

10 alts after pruning (6 fresh and 4 done)

	Kept	Total
New	0	0
Fresh	6	6
Picked	1	1
Done	3	3
Total	10	10

Error

4.9b

Counts

10 → 10

Alt Table

Status	Error	Program
✓	45.2b	(-.f64 (/.f64 c b) (/.f64 b a))
✓	45.0b	(/.f64 (neg.f64 b) a)
✓	36.3b	(neg.f64 (/.f64 c b))
	49.7b	(/.f64 (/.f64 (-.f64 (.f64 b b) (fma.f64 b b (.f64 -4 (.f64 a c)))) (-.f64 b (sqrt.f64 (fma.f64 b b (.f64 -4 (.f64 a c)))))) (.f64 2 a))
	55.2b	(/.f64 (+.f64 (neg.f64 b) b) (*.f64 2 a))
✓	38.2b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))
	57.2b	(cbrt.f64 (pow.f64 (.f64 (+.f64 b (sqrt.f64 (fma.f64 b b (.f64 -4 (*.f64 a c))))) (/.f64 1/2 a)) 3))
	49.4b	(pow.f64 (/.f64 (.f64 a 2) (+.f64 b (sqrt.f64 (fma.f64 b b (.f64 -4 (*.f64 a c)))))) -1)
	49.6b	(pow.f64 (cbrt.f64 (.f64 (+.f64 b (sqrt.f64 (fma.f64 b b (.f64 -4 (*.f64 a c))))) (/.f64 1/2 a))) 3)
	49.4b	(.f64 (/.f64 (sqrt.f64 (+.f64 b (sqrt.f64 (fma.f64 b b (.f64 -4 (.f64 a c)))))) a) (/.f64 (sqrt.f64 (+.f64 b (sqrt.f64 (fma.f64 b b (.f64 -4 (*.f64 a c)))))) 2))

Compiler

Compiled 180 to 120 computations (33.3% saved)

regimes752.0ms (14.3%)

Accuracy

Total 4.4b remaining (44.5%)

Threshold costs 0b (0%)

Counts

59 → 3

Compiler

Compiled 4984 to 3378 computations (32.2% saved)

bsearch78.0ms (1.5%)

Steps

Iters	Range		Point
10	4.241946271543068e-138	4.350640292110055e-126	4.1779810674765516e-126
9	-1.1141153340912374e+99	-1.146861339112528e+94	-1.0963394235440253e+99

Compiler

Compiled 4 to 3 computations (25% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

10×	`+-commutative_binary64`
10×	`*-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	26	54
1	45	52
2	70	52
3	82	52
4	88	52
5	89	52
6	88	52

end121.0ms (2.3%)

Compiler: Compiled 256 to 166 computations (35.2% saved)

Details

analyze618.0ms (11.8%)

sample2.9s (54.8%)

simplify256.0ms (4.9%)

prune3.0ms (0.1%)

localize10.0ms (0.2%)

series126.0ms (2.4%)

rewrite131.0ms (2.5%)

simplify78.0ms (1.5%)

prune162.0ms (3.1%)

localize3.0ms (0.1%)

prune10.0ms (0.2%)

localize3.0ms (0.1%)

prune9.0ms (0.2%)

localize4.0ms (0.1%)

prune6.0ms (0.1%)

regimes752.0ms (14.3%)

bsearch78.0ms (1.5%)

simplify4.0ms (0.1%)

end121.0ms (2.3%)

Profiling