Details

analyze88.0ms (3.3%)

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
25%	74.9%	0.1%	5
37.5%	50%	12.6%	6
50%	37.5%	12.6%	7
56.2%	25%	18.8%	8
62.4%	18.7%	18.8%	9
65.6%	12.5%	22%	10
68.7%	9.4%	22%	11
70.2%	6.2%	23.5%	12
71.8%	4.7%	23.5%	13
72.6%	3.1%	24.3%	14

Compiler

Compiled 10 to 7 computations (30% saved)

sample829.0ms (30.5%)

Results

808.0ms	8256×	body	128	valid
8.0ms	94×	body	128	invalid

Compiler

Compiled 20 to 14 computations (30% saved)

preprocess34.0ms (1.2%)

Algorithm

2×	egg-herbie

Rules

496×	`fma-def_binary64`
136×	`fma-neg_binary64`
71×	`distribute-rgt-in_binary64`
53×	`unsub-neg_binary64`
46×	`distribute-lft-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	20
1	26	20
2	48	20
3	108	20
4	253	20
5	367	20
6	499	20
7	685	20
8	1198	20
9	1223	20
10	1273	20
0	2	2

Stop Event

1×	saturated
1×	saturated

Compiler

Compiled 9 to 6 computations (33.3% saved)

simplify14.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

265×	`fma-def_binary64`
84×	`fma-neg_binary64`
35×	`distribute-rgt-in_binary64`
25×	`unsub-neg_binary64`
24×	`sub-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	16	10
2	33	10
3	71	10
4	161	10
5	238	10
6	325	10
7	429	10
8	669	10
9	714	10
10	746	10

Stop Event

1×

saturated

Counts

1 → 2

prune7.0ms (0.2%)

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

0.1b

Counts

3 → 2

Alt Table

Status	Error	Program
	5.6b	(-.f64 x (.f64 y (.f64 x x)))
▶	0.1b	(.f64 x (-.f64 1 (.f64 x y)))

Compiler

Compiled 52 to 31 computations (40.4% saved)

localize4.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 x (-.f64 1 (.f64 x y)))

series7.0ms (0.3%)

Counts

1 → 24

Calls

6 calls:

2.0ms	(.f64 x (-.f64 1 (.f64 x y)))	y	-inf
1.0ms	(.f64 x (-.f64 1 (.f64 x y)))	x	-inf
1.0ms	(.f64 x (-.f64 1 (.f64 x y)))	x	0
1.0ms	(.f64 x (-.f64 1 (.f64 x y)))	x	inf
1.0ms	(.f64 x (-.f64 1 (.f64 x y)))	y	inf

rewrite39.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

682×	`log1p-expm1-u_binary64`
682×	`expm1-log1p-u_binary64`
423×	`prod-diff_binary64`
73×	`add-sqr-sqrt_binary64`
68×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	146	10
2	1841	10

Stop Event

1×	node limit

Counts

1 → 21

simplify37.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

1023×	`fma-neg_binary64`
478×	`cancel-sign-sub-inv_binary64`
266×	`associate-l_binary64`
251×	`unswap-sqr_binary64`
205×	`distribute-rgt-neg-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	218
1	23	218
2	50	218
3	124	218
4	349	218
5	1199	218
6	2253	218
7	3990	218

Stop Event

1×	node limit

Counts

45 → 26

prune20.0ms (0.7%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	22	4	26
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	23	5	28

Error

0.0b

Counts

28 → 5

Alt Table

Status	Error	Program
▶	0.1b	(-.f64 x (.f64 x (.f64 x y)))
	5.6b	(-.f64 x (.f64 y (.f64 x x)))
	30.8b	(pow.f64 (sqrt.f64 (.f64 x (-.f64 1 (.f64 x y)))) 2)
	1.3b	(pow.f64 (cbrt.f64 (.f64 x (-.f64 1 (.f64 x y)))) 3)
	7.6b	(/.f64 (.f64 (-.f64 1 (pow.f64 (.f64 x y) 2)) x) (+.f64 1 (*.f64 x y)))

Compiler

Compiled 389 to 229 computations (41.1% saved)

localize4.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 x (.f64 x (.f64 x y)))
✓	0.2b	(.f64 x (.f64 x y))

series15.0ms (0.6%)

Counts

2 → 48

Calls

12 calls:

2.0ms	(.f64 x (.f64 x y))	y	-inf
1.0ms	(.f64 x (.f64 x y))	y	0
1.0ms	(.f64 x (.f64 x y))	y	inf
1.0ms	(-.f64 x (.f64 x (.f64 x y)))	y	inf
1.0ms	(-.f64 x (.f64 x (.f64 x y)))	y	-inf

rewrite61.0ms (2.3%)

Algorithm

1×	batch-egg-rewrite

Rules

731×	`prod-diff_binary64`
704×	`log1p-expm1-u_binary64`
704×	`expm1-log1p-u_binary64`
130×	`egg-rr`
73×	`associate-r_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	17
1	134	17
2	1919	17

Stop Event

1×	node limit

Counts

2 → 130

simplify42.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

1024×	`fma-neg_binary64`
480×	`cancel-sign-sub-inv_binary64`
261×	`associate-l_binary64`
251×	`unswap-sqr_binary64`
205×	`distribute-rgt-neg-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	386
1	23	386
2	50	386
3	124	386
4	349	386
5	1191	386
6	2249	386
7	3988	386

Stop Event

1×	node limit

Counts

178 → 137

prune99.0ms (3.7%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	134	3	137
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	134	8	142

Error

Counts

142 → 8

Alt Table

Status	Error	Program
✓	0.1b	(-.f64 x (.f64 x (.f64 x y)))
	5.6b	(-.f64 x (.f64 y (.f64 x x)))
	34.9b	(-.f64 x (pow.f64 (*.f64 x (sqrt.f64 y)) 2))
	30.8b	(pow.f64 (sqrt.f64 (.f64 x (-.f64 1 (.f64 x y)))) 2)
	1.3b	(pow.f64 (cbrt.f64 (.f64 x (-.f64 1 (.f64 x y)))) 3)
	7.6b	(/.f64 (.f64 (-.f64 1 (pow.f64 (.f64 x y) 2)) x) (+.f64 1 (*.f64 x y)))
▶	0.4b	(+.f64 (fma.f64 x 1 (neg.f64 (.f64 (cbrt.f64 x) (.f64 (.f64 x y) (pow.f64 (cbrt.f64 x) 2))))) (fma.f64 (neg.f64 (cbrt.f64 x)) (.f64 (.f64 x y) (pow.f64 (cbrt.f64 x) 2)) (.f64 (cbrt.f64 x) (.f64 (.f64 x y) (pow.f64 (cbrt.f64 x) 2)))))
	25.4b	(+.f64 (fma.f64 x 1 (neg.f64 (.f64 (.f64 (sqrt.f64 (.f64 x y)) x) (sqrt.f64 (.f64 x y))))) (fma.f64 (neg.f64 (.f64 (sqrt.f64 (.f64 x y)) x)) (sqrt.f64 (.f64 x y)) (.f64 (.f64 (sqrt.f64 (.f64 x y)) x) (sqrt.f64 (*.f64 x y)))))

Compiler

Compiled 3832 to 1150 computations (70% saved)

localize14.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (cbrt.f64 x) (.f64 (*.f64 x y) (pow.f64 (cbrt.f64 x) 2)))
✓	0.5b	(pow.f64 (cbrt.f64 x) 2)
✓	0.6b	(cbrt.f64 x)
✓	40.0b	(fma.f64 (neg.f64 (cbrt.f64 x)) (.f64 (.f64 x y) (pow.f64 (cbrt.f64 x) 2)) (.f64 (cbrt.f64 x) (.f64 (*.f64 x y) (pow.f64 (cbrt.f64 x) 2))))

series324.0ms (11.9%)

Counts

4 → 39

Calls

18 calls:

65.0ms	(fma.f64 (neg.f64 (cbrt.f64 x)) (.f64 (.f64 x y) (pow.f64 (cbrt.f64 x) 2)) (.f64 (cbrt.f64 x) (.f64 (*.f64 x y) (pow.f64 (cbrt.f64 x) 2))))	y	0
64.0ms	(fma.f64 (neg.f64 (cbrt.f64 x)) (.f64 (.f64 x y) (pow.f64 (cbrt.f64 x) 2)) (.f64 (cbrt.f64 x) (.f64 (*.f64 x y) (pow.f64 (cbrt.f64 x) 2))))	y	-inf
61.0ms	(fma.f64 (neg.f64 (cbrt.f64 x)) (.f64 (.f64 x y) (pow.f64 (cbrt.f64 x) 2)) (.f64 (cbrt.f64 x) (.f64 (*.f64 x y) (pow.f64 (cbrt.f64 x) 2))))	y	inf
50.0ms	(.f64 (cbrt.f64 x) (.f64 (*.f64 x y) (pow.f64 (cbrt.f64 x) 2)))	x	-inf
33.0ms	(fma.f64 (neg.f64 (cbrt.f64 x)) (.f64 (.f64 x y) (pow.f64 (cbrt.f64 x) 2)) (.f64 (cbrt.f64 x) (.f64 (*.f64 x y) (pow.f64 (cbrt.f64 x) 2))))	x	-inf

rewrite53.0ms (1.9%)

Algorithm

1×	batch-egg-rewrite

Rules

860×	`expm1-log1p-u_binary64`
785×	`prod-diff_binary64`
120×	`associate-r_binary64`
110×	`add-sqr-sqrt_binary64`
103×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	62
1	227	32
2	2785	32

Stop Event

1×	node limit

Counts

4 → 94

simplify64.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

607×	`sqr-pow_binary64`
445×	`associate-l_binary64`
434×	`unswap-sqr_binary64`
281×	`cube-prod_binary64`
273×	`fabs-mul_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	201
1	13	201
2	23	201
3	44	201
4	107	201
5	336	201
6	1237	201
7	2113	201
8	2277	201
9	2461	201
10	2669	201
11	2960	201
12	3353	201
13	3833	201
14	4396	201

Stop Event

1×	node limit

Counts

133 → 97

prune440.0ms (16.2%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	333	0	333
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	333	8	341

Error

Counts

341 → 8

Alt Table

Status	Error	Program
✓	0.1b	(-.f64 x (.f64 x (.f64 x y)))
	5.6b	(-.f64 x (.f64 y (.f64 x x)))
	34.9b	(-.f64 x (pow.f64 (*.f64 x (sqrt.f64 y)) 2))
	30.8b	(pow.f64 (sqrt.f64 (.f64 x (-.f64 1 (.f64 x y)))) 2)
▶	1.3b	(pow.f64 (cbrt.f64 (.f64 x (-.f64 1 (.f64 x y)))) 3)
	7.6b	(/.f64 (.f64 (-.f64 1 (pow.f64 (.f64 x y) 2)) x) (+.f64 1 (*.f64 x y)))
✓	0.4b	(+.f64 (fma.f64 x 1 (neg.f64 (.f64 (cbrt.f64 x) (.f64 (.f64 x y) (pow.f64 (cbrt.f64 x) 2))))) (fma.f64 (neg.f64 (cbrt.f64 x)) (.f64 (.f64 x y) (pow.f64 (cbrt.f64 x) 2)) (.f64 (cbrt.f64 x) (.f64 (.f64 x y) (pow.f64 (cbrt.f64 x) 2)))))
	25.4b	(+.f64 (fma.f64 x 1 (neg.f64 (.f64 (.f64 (sqrt.f64 (.f64 x y)) x) (sqrt.f64 (.f64 x y))))) (fma.f64 (neg.f64 (.f64 (sqrt.f64 (.f64 x y)) x)) (sqrt.f64 (.f64 x y)) (.f64 (.f64 (sqrt.f64 (.f64 x y)) x) (sqrt.f64 (*.f64 x y)))))

Compiler

Compiled 14121 to 6107 computations (56.8% saved)

localize7.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.1b	(.f64 x (-.f64 1 (.f64 x y)))
✓	0.6b	(cbrt.f64 (.f64 x (-.f64 1 (.f64 x y))))
✓	0.7b	(pow.f64 (cbrt.f64 (.f64 x (-.f64 1 (.f64 x y)))) 3)

series133.0ms (4.9%)

Counts

2 → 8

Calls

12 calls:

82.0ms	(pow.f64 (cbrt.f64 (.f64 x (-.f64 1 (.f64 x y)))) 3)	y	0
18.0ms	(pow.f64 (cbrt.f64 (.f64 x (-.f64 1 (.f64 x y)))) 3)	x	-inf
12.0ms	(cbrt.f64 (.f64 x (-.f64 1 (.f64 x y))))	x	-inf
3.0ms	(pow.f64 (cbrt.f64 (.f64 x (-.f64 1 (.f64 x y)))) 3)	y	-inf
3.0ms	(pow.f64 (cbrt.f64 (.f64 x (-.f64 1 (.f64 x y)))) 3)	x	0

rewrite52.0ms (1.9%)

Algorithm

1×	batch-egg-rewrite

Rules

845×	`log1p-expm1-u_binary64`
845×	`expm1-log1p-u_binary64`
423×	`prod-diff_binary64`
91×	`add-sqr-sqrt_binary64`
87×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	22
1	207	22
2	2334	22

Stop Event

1×	node limit

Counts

2 → 65

simplify30.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

566×	`unswap-sqr_binary64`
550×	`cancel-sign-sub-inv_binary64`
539×	`fma-def_binary64`
279×	`*-commutative_binary64`
236×	`distribute-rgt-neg-in_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	37	216
1	119	216
2	336	214
3	1259	211
4	4109	163

Stop Event

1×	node limit

Counts

73 → 76

prune65.0ms (2.4%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	101	1	102
Fresh	1	4	5
Picked	0	1	1
Done	0	2	2
Total	102	8	110

Error

Counts

110 → 8

Alt Table

Status	Error	Program
	0.5b	(.f64 (pow.f64 (cbrt.f64 (-.f64 1 (.f64 x y))) 2) (.f64 (cbrt.f64 (-.f64 1 (.f64 x y))) x))
	7.6b	(/.f64 (.f64 (-.f64 1 (pow.f64 (.f64 x y) 2)) x) (+.f64 1 (*.f64 x y)))
✓	0.1b	(-.f64 x (.f64 x (.f64 x y)))
	5.6b	(-.f64 x (.f64 y (.f64 x x)))
	34.9b	(-.f64 x (pow.f64 (*.f64 x (sqrt.f64 y)) 2))
	30.8b	(pow.f64 (sqrt.f64 (.f64 x (-.f64 1 (.f64 x y)))) 2)
✓	1.3b	(pow.f64 (cbrt.f64 (.f64 x (-.f64 1 (.f64 x y)))) 3)
✓	0.4b	(+.f64 (fma.f64 x 1 (neg.f64 (.f64 (cbrt.f64 x) (.f64 (.f64 x y) (pow.f64 (cbrt.f64 x) 2))))) (fma.f64 (neg.f64 (cbrt.f64 x)) (.f64 (.f64 x y) (pow.f64 (cbrt.f64 x) 2)) (.f64 (cbrt.f64 x) (.f64 (.f64 x y) (pow.f64 (cbrt.f64 x) 2)))))

Compiler

Compiled 1663 to 1048 computations (37% saved)

regimes130.0ms (4.8%)

Accuracy

Total 0.1b remaining (83.3%)

Threshold costs 0.1b (83.3%)

Counts

33 → 1

Compiler

Compiled 2118 to 1160 computations (45.2% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

6×	`*-commutative_binary64`
5×	`+-commutative_binary64`
5×	`sub-neg_binary64`
4×	`distribute-rgt-neg-in_binary64`
4×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	10
1	13	10
2	25	10
3	36	10
4	42	10
5	45	10
6	46	10

Stop Event

1×

saturated

end101.0ms (3.7%)

Stop Event

1×

fuel

Compiler

Compiled 147 to 90 computations (38.8% saved)

Iter	Nodes	Cost
0	7	10
1	16	10
2	33	10
3	71	10
4	161	10
5	238	10
6	325	10
7	429	10
8	669	10
9	714	10
10	746	10

Iter	Nodes	Cost
0	7	10
1	16	10
2	33	10
3	71	10
4	161	10
5	238	10
6	325	10
7	429	10
8	669	10
9	714	10
10	746	10

Details

analyze88.0ms (3.3%)

sample829.0ms (30.5%)

preprocess34.0ms (1.2%)

simplify14.0ms (0.5%)

prune7.0ms (0.2%)

localize4.0ms (0.2%)

series7.0ms (0.3%)

rewrite39.0ms (1.4%)

simplify37.0ms (1.4%)

prune20.0ms (0.7%)

localize4.0ms (0.2%)

series15.0ms (0.6%)

rewrite61.0ms (2.3%)

simplify42.0ms (1.5%)

prune99.0ms (3.7%)

localize14.0ms (0.5%)

series324.0ms (11.9%)

rewrite53.0ms (1.9%)

simplify64.0ms (2.4%)

prune440.0ms (16.2%)

localize7.0ms (0.3%)

series133.0ms (4.9%)

rewrite52.0ms (1.9%)

simplify30.0ms (1.1%)

prune65.0ms (2.4%)

regimes130.0ms (4.8%)

simplify3.0ms (0.1%)

end101.0ms (3.7%)

Profiling

Iter	Nodes	Cost
0	7	10
1	16	10
2	33	10
3	71	10
4	161	10
5	238	10
6	325	10
7	429	10
8	669	10
9	714	10
10	746	10