Details

analyze1.1s (13.4%)

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
18.7%	76.5%	4.8%	7
28.1%	66.3%	5.6%	8
34.7%	55.4%	9.9%	9
36.1%	51.1%	12.8%	10
42.1%	42.4%	15.5%	11
47.5%	33.8%	18.7%	12
48.8%	30.7%	20.6%	13
51.8%	25.6%	22.5%	14

Compiler

Compiled 17 to 11 computations (35.3% saved)

sample4.5s (54.5%)

Results

1.3s	1179×	body	2048	valid
1.2s	5338×	body	128	valid
517.0ms	755×	body	1024	valid
471.0ms	437×	body	4096	valid
307.0ms	378×	body	512	valid
239.0ms	1071×	body	128	invalid
65.0ms	169×	body	256	valid

Compiler

Compiled 50 to 32 computations (36% saved)

simplify98.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

808×	`fma-neg_binary64`
379×	`associate-/l*_binary64`
361×	`div-sub_binary64`
341×	`fma-def_binary64`
224×	`times-frac_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	20
1	23	18
2	39	18
3	69	18
4	107	18
5	178	18
6	279	18
7	382	18
8	547	18
9	587	18
10	855	18
11	1247	18
12	1117	18
13	1035	18
14	1043	18
15	1051	18
16	1077	18
17	1093	18
18	1129	18
19	1131	18
20	1143	18
21	1050	18

prune5.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	2	1	3

Error

36.5b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	36.5b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)

Compiler

Compiled 58 to 30 computations (48.3% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)
✓	0.6b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
✓	0.6b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
✓	24.1b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

series334.0ms (4%)

Counts

4 → 96

Calls

4 calls:

145.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)
95.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
77.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
16.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

rewrite119.0ms (1.4%)

Algorithm

2×	batch-egg-rewrite

Rules

700×	`fma-def_binary64`
338×	`fma-neg_binary64`
313×	`egg-rr`
216×	`expm1-udef_binary64`
216×	`log1p-udef_binary64`

Counts

4 → 313

Calls

4 calls:

112.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)
112.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
112.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
112.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	55
1	234	55
2	3299	55
3	4945	55
0	0	0
1	0	0

simplify64.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

738×	`times-frac_binary64`
493×	`associate-/l*_binary64`
403×	`associate-/r*_binary64`
361×	`fma-def_binary64`
191×	`associate-*l/_binary64`

Counts

409 → 381

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	120	2203
1	388	2175
2	1292	2133
3	4966	2133

prune196.0ms (2.4%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	372	9	381
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	372	10	382

Error

4.1b

Counts

382 → 10

Alt Table

Status	Error	Program
	36.9b	(*.f64 -1/2 (/.f64 c b_2))
✓	36.5b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)
	36.9b	(.f64 (pow.f64 (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)) 2) (.f64 (cbrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)) (/.f64 1 a)))
▶	36.5b	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2) (/.f64 1 a))
	51.1b	(cbrt.f64 (pow.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a) 3))
	45.1b	(/.f64 (-.f64 (cbrt.f64 (pow.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)) 3/2)) b_2) a)
	37.4b	(/.f64 (-.f64 (pow.f64 (pow.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)) 1/4) 2) b_2) a)
	44.9b	(fma.f64 1/2 (/.f64 c b_2) (*.f64 -2 (/.f64 b_2 a)))
	44.7b	(*.f64 -2 (/.f64 b_2 a))
	42.1b	(fma.f64 -1/2 (/.f64 c b_2) (.f64 (/.f64 (.f64 c (*.f64 c a)) (pow.f64 b_2 3)) -1/8))

Compiler

Compiled 9493 to 2881 computations (69.7% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2) (/.f64 1 a))
	0.6b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
	0.6b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
	24.1b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

series80.0ms (1%)

Counts

1 → 20

Calls

1 calls:

80.0ms

(*.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2) (/.f64 1 a))

rewrite64.0ms (0.8%)

Algorithm

2×	batch-egg-rewrite

Rules

699×	`fma-def_binary64`
320×	`fma-neg_binary64`
230×	`expm1-udef_binary64`
230×	`log1p-udef_binary64`
133×	`add-sqr-sqrt_binary64`

Counts

1 → 43

Calls

1 calls:

62.0ms

(*.f64 (-.f64 (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c))) b_2) (/.f64 1 a))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	18
1	267	18
2	3403	18
3	5037	18
0	0	0
1	0	0

simplify45.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

881×	`fma-neg_binary64`
363×	`times-frac_binary64`
351×	`unswap-sqr_binary64`
239×	`associate-/l*_binary64`
217×	`associate-r_binary64`

Counts

63 → 64

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	65	654
1	204	642
2	668	624
3	3419	624
4	4941	624

prune193.0ms (2.3%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	376	2	378
Fresh	4	4	8
Picked	0	1	1
Done	0	1	1
Total	380	8	388

Error

4.1b

Counts

388 → 8

Alt Table

Status	Error	Program
▶	36.9b	(*.f64 -1/2 (/.f64 c b_2))
✓	36.5b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)
	44.9b	(fma.f64 1/2 (/.f64 c b_2) (*.f64 -2 (/.f64 b_2 a)))
	46.6b	(/.f64 (.f64 (-.f64 (.f64 b_2 b_2) (fma.f64 b_2 b_2 (.f64 a c))) (/.f64 1 a)) (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))))
	42.1b	(fma.f64 -1/2 (/.f64 c b_2) (.f64 (/.f64 (.f64 c (*.f64 c a)) (pow.f64 b_2 3)) -1/8))
	49.7b	(/.f64 (-.f64 (.f64 b_2 b_2) (fma.f64 b_2 b_2 (.f64 a c))) (.f64 a (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))))))
✓	36.5b	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2) (/.f64 1 a))
	44.7b	(*.f64 -2 (/.f64 b_2 a))

Compiler

Compiled 9946 to 3464 computations (65.2% saved)

localize3.0ms (0%)

prune6.0ms (0.1%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Kept	Total
New	0	0
Fresh	5	5
Picked	1	1
Done	2	2
Total	8	8

Error

4.1b

Counts

8 → 8

Alt Table

Status	Error	Program
✓	36.9b	(*.f64 -1/2 (/.f64 c b_2))
✓	36.5b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)
	44.9b	(fma.f64 1/2 (/.f64 c b_2) (*.f64 -2 (/.f64 b_2 a)))
	46.6b	(/.f64 (.f64 (-.f64 (.f64 b_2 b_2) (fma.f64 b_2 b_2 (.f64 a c))) (/.f64 1 a)) (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))))
▶	42.1b	(fma.f64 -1/2 (/.f64 c b_2) (.f64 (/.f64 (.f64 c (*.f64 c a)) (pow.f64 b_2 3)) -1/8))
	49.7b	(/.f64 (-.f64 (.f64 b_2 b_2) (fma.f64 b_2 b_2 (.f64 a c))) (.f64 a (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))))))
✓	36.5b	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2) (/.f64 1 a))
	44.7b	(*.f64 -2 (/.f64 b_2 a))

Compiler

Compiled 228 to 134 computations (41.2% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 c (.f64 c a))
✓	0.2b	(.f64 (/.f64 (.f64 c (*.f64 c a)) (pow.f64 b_2 3)) -1/8)
✓	4.5b	(fma.f64 -1/2 (/.f64 c b_2) (.f64 (/.f64 (.f64 c (*.f64 c a)) (pow.f64 b_2 3)) -1/8))
✓	15.7b	(/.f64 (.f64 c (.f64 c a)) (pow.f64 b_2 3))

series239.0ms (2.9%)

Counts

4 → 132

Calls

4 calls:

88.0ms	(.f64 (/.f64 (.f64 c (*.f64 c a)) (pow.f64 b_2 3)) -1/8)
75.0ms	(fma.f64 -1/2 (/.f64 c b_2) (.f64 (/.f64 (.f64 c (*.f64 c a)) (pow.f64 b_2 3)) -1/8))
67.0ms	(/.f64 (.f64 c (.f64 c a)) (pow.f64 b_2 3))
8.0ms	(.f64 c (.f64 c a))

rewrite74.0ms (0.9%)

Algorithm

2×	batch-egg-rewrite

Rules

257×	`expm1-udef_binary64`
257×	`log1p-udef_binary64`
225×	`prod-diff_binary64`
145×	`add-sqr-sqrt_binary64`
136×	`add-cbrt-cube_binary64`

Counts

4 → 117

Calls

4 calls:

72.0ms	(.f64 c (.f64 c a))
72.0ms	(.f64 (/.f64 (.f64 c (*.f64 c a)) (pow.f64 b_2 3)) -1/8)
72.0ms	(fma.f64 -1/2 (/.f64 c b_2) (.f64 (/.f64 (.f64 c (*.f64 c a)) (pow.f64 b_2 3)) -1/8))
72.0ms	(/.f64 (.f64 c (.f64 c a)) (pow.f64 b_2 3))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	59
1	298	59
2	3750	59
3	4924	59
0	0	0
1	0	0

simplify78.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

759×	`distribute-neg-frac_binary64`
723×	`fma-neg_binary64`
596×	`times-frac_binary64`
531×	`associate-/l*_binary64`
338×	`associate-*l/_binary64`

Counts

249 → 126

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	21	1995
1	57	1995
2	173	1941
3	735	1941
4	3952	1941
5	5336	1941

prune71.0ms (0.9%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	125	1	126
Fresh	0	4	4
Picked	1	0	1
Done	0	3	3
Total	126	8	134

Error

4.1b

Counts

134 → 8

Alt Table

Status	Error	Program
✓	36.9b	(*.f64 -1/2 (/.f64 c b_2))
✓	36.5b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)
	44.9b	(fma.f64 1/2 (/.f64 c b_2) (*.f64 -2 (/.f64 b_2 a)))
	46.6b	(/.f64 (.f64 (-.f64 (.f64 b_2 b_2) (fma.f64 b_2 b_2 (.f64 a c))) (/.f64 1 a)) (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))))
✓	36.5b	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2) (/.f64 1 a))
	51.1b	(exp.f64 (log.f64 (fma.f64 -1/2 (/.f64 c b_2) (.f64 (/.f64 (.f64 c (*.f64 c a)) (pow.f64 b_2 3)) -1/8))))
	44.7b	(*.f64 -2 (/.f64 b_2 a))
	49.7b	(/.f64 (-.f64 (.f64 b_2 b_2) (fma.f64 b_2 b_2 (.f64 a c))) (.f64 a (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))))))

Compiler

Compiled 2624 to 1302 computations (50.4% saved)

regimes778.0ms (9.4%)

Accuracy

Total 4.3b remaining (43.6%)

Threshold costs 0b (0%)

Counts

58 → 3

Compiler

Compiled 4512 to 2702 computations (40.1% saved)

bsearch65.0ms (0.8%)

Steps

Iters	Range		Point
7	4.2374538254161256e-109	1.3010807537774533e-107	8.69056174658403e-108
11	-4.720205408789769e+163	-1.36470186509095e+135	-2.6219979828528404e+149

Compiler

Compiled 4 to 3 computations (25% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	44
1	33	44
2	46	44
3	54	44
4	59	44
5	60	44
6	60	44

end106.0ms (1.3%)

Compiler: Compiled 202 to 124 computations (38.6% saved)

Details

analyze1.1s (13.4%)

sample4.5s (54.5%)

simplify98.0ms (1.2%)

prune5.0ms (0.1%)

localize14.0ms (0.2%)

series334.0ms (4%)

rewrite119.0ms (1.4%)

simplify64.0ms (0.8%)

prune196.0ms (2.4%)

localize8.0ms (0.1%)

series80.0ms (1%)

rewrite64.0ms (0.8%)

simplify45.0ms (0.6%)

prune193.0ms (2.3%)

localize3.0ms (0%)

prune6.0ms (0.1%)

localize10.0ms (0.1%)

series239.0ms (2.9%)

rewrite74.0ms (0.9%)

simplify78.0ms (0.9%)

prune71.0ms (0.9%)

regimes778.0ms (9.4%)

bsearch65.0ms (0.8%)

simplify3.0ms (0%)

end106.0ms (1.3%)

Profiling