Details

analyze2.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	50%	0%	2
50%	25%	25%	3
50%	12.5%	37.5%	4
50%	6.2%	43.8%	5
50%	3.1%	46.9%	6
50%	1.6%	48.5%	7
50%	0.8%	49.2%	8
50%	0.4%	49.6%	9
50%	0.2%	49.8%	10
50%	0.1%	49.9%	11
50%	0%	50%	12
50%	0%	50%	13
50%	0%	50%	14

Compiler

Compiled 9 to 7 computations (22.2% saved)

sample1.4s (46.3%)

Results

594.0ms	2090×	body	1024	valid
371.0ms	4338×	body	128	valid
228.0ms	1060×	body	512	valid
79.0ms	543×	body	256	valid
74.0ms	225×	body	2048	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 26 to 20 computations (23.1% saved)

simplify9.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

39×	`fma-def_binary64`
32×	`fma-neg_binary64`
15×	`cancel-sign-sub-inv_binary64`
12×	`sub-neg_binary64`
10×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	12	11
2	16	11
3	23	11
4	32	11
5	49	11
6	86	11
7	123	11
8	166	11
9	202	11
10	228	11
11	230	11

Stop Event

1×

saturated

Counts

1 → 1

prune1.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

31.5b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	31.5b	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

Compiler

Compiled 24 to 18 computations (25% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (+.f64 x 1))
✓	2.8b	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

series15.0ms (0.5%)

Counts

2 → 5

Calls

2 calls:

10.0ms	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
5.0ms	(sqrt.f64 (+.f64 x 1))

rewrite51.0ms (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

832×	`prod-diff_binary64`
742×	`log1p-expm1-u_binary64`
742×	`expm1-log1p-u_binary64`
114×	`egg-rr`
72×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	17
1	153	17
2	2027	17

Stop Event

1×	node limit

Counts

2 → 114

Calls

2 calls:

49.0ms	(sqrt.f64 (+.f64 x 1))
49.0ms	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

simplify36.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

664×	`fma-def_binary64`
612×	`associate-l_binary64`
536×	`unswap-sqr_binary64`
370×	`associate-r_binary64`
222×	`fma-neg_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	18	48
1	51	44
2	123	38
3	394	34
4	1126	29
5	3744	29

Stop Event

1×	node limit

Counts

119 → 121

prune143.0ms (4.8%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	111	10	121
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	112	10	122

Error

30.1b

Counts

122 → 10

Alt Table

Status	Error	Program
	31.8b	(/.f64 (+.f64 (pow.f64 (+.f64 x 1) 3/2) (pow.f64 (neg.f64 (sqrt.f64 x)) 3)) (+.f64 (+.f64 x 1) (-.f64 (.f64 (neg.f64 (sqrt.f64 x)) (neg.f64 (sqrt.f64 x))) (.f64 (sqrt.f64 (+.f64 x 1)) (neg.f64 (sqrt.f64 x))))))
	31.5b	(fma.f64 (pow.f64 (+.f64 x 1) 1/4) (pow.f64 (+.f64 x 1) 1/4) (neg.f64 (sqrt.f64 x)))
▶	31.1b	(/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
	31.7b	(+.f64 (fma.f64 (pow.f64 (+.f64 x 1) 1/4) (pow.f64 (+.f64 x 1) 1/4) (neg.f64 (.f64 (sqrt.f64 (cbrt.f64 x)) (sqrt.f64 (pow.f64 (cbrt.f64 x) 2))))) (fma.f64 (neg.f64 (sqrt.f64 (cbrt.f64 x))) (sqrt.f64 (pow.f64 (cbrt.f64 x) 2)) (.f64 (sqrt.f64 (cbrt.f64 x)) (sqrt.f64 (pow.f64 (cbrt.f64 x) 2)))))
	31.4b	(+.f64 (fma.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 x 1)) 2)) (sqrt.f64 (cbrt.f64 (+.f64 x 1))) (neg.f64 (sqrt.f64 x))) (fma.f64 (neg.f64 (pow.f64 x 1/4)) (pow.f64 x 1/4) (sqrt.f64 x)))
	31.5b	(+.f64 (fma.f64 (cbrt.f64 (sqrt.f64 (+.f64 x 1))) (cbrt.f64 (+.f64 x 1)) (neg.f64 (sqrt.f64 x))) (fma.f64 (neg.f64 (pow.f64 x 1/4)) (pow.f64 x 1/4) (sqrt.f64 x)))
	31.5b	(+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (fma.f64 (neg.f64 (pow.f64 x 1/4)) (pow.f64 x 1/4) (sqrt.f64 x)))
	31.7b	(+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (fma.f64 (neg.f64 (cbrt.f64 (sqrt.f64 x))) (cbrt.f64 x) (sqrt.f64 x)))
	32.6b	1
	31.3b	(/.f64 (-.f64 (+.f64 x 1) (*.f64 (neg.f64 (sqrt.f64 x)) (neg.f64 (sqrt.f64 x)))) (-.f64 (sqrt.f64 (+.f64 x 1)) (neg.f64 (sqrt.f64 x))))

Compiler

Compiled 2842 to 1799 computations (36.7% saved)

localize8.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(sqrt.f64 (+.f64 x 1))
✓	0.0b	(+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
✓	0.1b	(/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
✓	2.4b	(+.f64 x (-.f64 1 x))

series21.0ms (0.7%)

Counts

3 → 14

Calls

3 calls:

11.0ms	(+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
9.0ms	(/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
1.0ms	(+.f64 x (-.f64 1 x))

rewrite81.0ms (2.7%)

Algorithm

1×	batch-egg-rewrite

Rules

689×	`fma-def_binary64`
347×	`fma-neg_binary64`
275×	`egg-rr`
199×	`expm1-udef_binary64`
199×	`log1p-udef_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	38
1	237	29
2	3535	29

Stop Event

1×	node limit

Counts

3 → 275

Calls

3 calls:

76.0ms	(+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
76.0ms	(/.f64 (+.f64 x (-.f64 1 x)) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
76.0ms	(+.f64 x (-.f64 1 x))

simplify14.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1	14
1	4	14

Stop Event

1×

saturated

Counts

289 → 276

prune252.0ms (8.5%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	304	4	308
Fresh	9	0	9
Picked	1	0	1
Done	0	0	0
Total	314	4	318

Error

0.1b

Counts

318 → 4

Alt Table

Status	Error	Program
	31.5b	(fma.f64 (sqrt.f64 (+.f64 x 1)) 1 (neg.f64 (sqrt.f64 x)))
▶	0.2b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
	31.1b	(cbrt.f64 (/.f64 (pow.f64 (+.f64 x (-.f64 1 x)) 3) (pow.f64 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) 3)))
	31.5b	(-.f64 (/.f64 (+.f64 x 1) (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))) (/.f64 x (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))))

Compiler

Compiled 6663 to 4225 computations (36.6% saved)

localize5.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(sqrt.f64 (+.f64 x 1))
	0.0b	(+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
✓	0.2b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))

series9.0ms (0.3%)

Counts

1 → 1

Calls

1 calls:

9.0ms

(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))

rewrite38.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

845×	`log1p-expm1-u_binary64`
845×	`expm1-log1p-u_binary64`
84×	`add-sqr-sqrt_binary64`
82×	`add-cbrt-cube_binary64`
79×	`add-log-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	14
1	178	14
2	2385	14

Stop Event

1×	node limit

Counts

1 → 25

Calls

1 calls:

37.0ms

(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))

simplify6.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1	1
1	4	1

Stop Event

1×

saturated

Counts

26 → 26

prune155.0ms (5.2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	98	9	107
Fresh	3	0	3
Picked	1	0	1
Done	0	0	0
Total	102	9	111

Error

0.0b

Counts

111 → 9

Alt Table

Status	Error	Program
	0.2b	(/.f64 1 (fma.f64 (pow.f64 x 1/4) (pow.f64 x 1/4) (sqrt.f64 (+.f64 x 1))))
	14.4b	(.f64 (/.f64 1 (+.f64 (pow.f64 (+.f64 1 x) 3/2) (pow.f64 x 3/2))) (-.f64 (+.f64 (+.f64 1 x) x) (sqrt.f64 (.f64 (+.f64 1 x) x))))
	0.3b	(/.f64 1 (fma.f64 (sqrt.f64 (pow.f64 (cbrt.f64 x) 2)) (sqrt.f64 (cbrt.f64 x)) (sqrt.f64 (+.f64 x 1))))
	0.5b	(*.f64 (/.f64 1 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (cbrt.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -2)))
▶	0.2b	(sqrt.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -2))
	0.3b	(pow.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -1/2) 2)
	0.5b	(*.f64 (pow.f64 (hypot.f64 (pow.f64 (+.f64 1 x) 1/4) (pow.f64 x 1/4)) -1) (pow.f64 (hypot.f64 (pow.f64 (+.f64 1 x) 1/4) (pow.f64 x 1/4)) -1))
	0.7b	(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 2) -1) (pow.f64 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) -1))
	7.9b	(cbrt.f64 (pow.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 3))

Compiler

Compiled 1869 to 1364 computations (27% saved)

localize6.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (+.f64 1 x))
✓	0.0b	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
✓	0.1b	(sqrt.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -2))
✓	0.3b	(pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -2)

series35.0ms (1.2%)

Counts

4 → 7

Calls

4 calls:

13.0ms	(pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -2)
9.0ms	(sqrt.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -2))
8.0ms	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
5.0ms	(sqrt.f64 (+.f64 1 x))

rewrite52.0ms (1.8%)

Algorithm

1×	batch-egg-rewrite

Rules

439×	`fma-def_binary64`
414×	`log-prod_binary64`
218×	`fma-neg_binary64`
171×	`expm1-udef_binary64`
171×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	45
1	217	45
2	2675	45

Stop Event

1×	node limit

Counts

4 → 134

Calls

4 calls:

50.0ms	(sqrt.f64 (+.f64 1 x))
50.0ms	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
50.0ms	(sqrt.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -2))
50.0ms	(pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -2)

simplify27.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

664×	`fma-def_binary64`
612×	`associate-l_binary64`
536×	`unswap-sqr_binary64`
370×	`associate-r_binary64`
222×	`fma-neg_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	18	50
1	51	46
2	123	40
3	394	36
4	1126	31
5	3744	31

Stop Event

1×	node limit

Counts

141 → 141

prune171.0ms (5.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	138	3	141
Fresh	4	4	8
Picked	0	1	1
Done	0	0	0
Total	142	8	150

Error

Counts

150 → 8

Alt Table

Status	Error	Program
	0.3b	(/.f64 1 (fma.f64 (sqrt.f64 (pow.f64 (cbrt.f64 x) 2)) (sqrt.f64 (cbrt.f64 x)) (sqrt.f64 (+.f64 x 1))))
	0.5b	(*.f64 (/.f64 1 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (cbrt.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -2)))
✓	0.2b	(sqrt.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -2))
	0.3b	(pow.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -1/2) 2)
	0.4b	(sqrt.f64 (pow.f64 (pow.f64 (hypot.f64 (pow.f64 (+.f64 1 x) 1/4) (pow.f64 x 1/4)) 2) -2))
	14.4b	(.f64 (/.f64 1 (+.f64 (pow.f64 (+.f64 1 x) 3/2) (pow.f64 x 3/2))) (-.f64 (+.f64 (+.f64 1 x) x) (sqrt.f64 (.f64 (+.f64 1 x) x))))
	20.2b	(sqrt.f64 (cbrt.f64 (pow.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -2) 3)))
	7.9b	(cbrt.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -3))

Compiler

Compiled 2371 to 1773 computations (25.2% saved)

regimes329.0ms (11%)

Accuracy

Total 0.1b remaining (84.7%)

Threshold costs 0.1b (84.7%)

Counts

181 → 1

Compiler

Compiled 5781 to 4506 computations (22.1% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
1×	`fabs-div_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	16
1	16	16

Stop Event

1×

saturated

end122.0ms (4.1%)

Compiler: Compiled 148 to 119 computations (19.6% saved)

Iter	Nodes	Cost
0	7	11
1	12	11
2	16	11
3	23	11
4	32	11
5	49	11
6	86	11
7	123	11
8	166	11
9	202	11
10	228	11
11	230	11

Iter	Nodes	Cost
0	7	11
1	12	11
2	16	11
3	23	11
4	32	11
5	49	11
6	86	11
7	123	11
8	166	11
9	202	11
10	228	11
11	230	11

Details

analyze2.0ms (0.1%)

sample1.4s (46.3%)

simplify9.0ms (0.3%)

prune1.0ms (0%)

localize6.0ms (0.2%)

series15.0ms (0.5%)

rewrite51.0ms (1.7%)

simplify36.0ms (1.2%)

prune143.0ms (4.8%)

localize8.0ms (0.3%)

series21.0ms (0.7%)

rewrite81.0ms (2.7%)

simplify14.0ms (0.5%)

prune252.0ms (8.5%)

localize5.0ms (0.2%)

series9.0ms (0.3%)

rewrite38.0ms (1.3%)

simplify6.0ms (0.2%)

prune155.0ms (5.2%)

localize6.0ms (0.2%)

series35.0ms (1.2%)

rewrite52.0ms (1.8%)

simplify27.0ms (0.9%)

prune171.0ms (5.8%)

regimes329.0ms (11%)

simplify2.0ms (0.1%)

end122.0ms (4.1%)

Profiling

Iter	Nodes	Cost
0	7	11
1	12	11
2	16	11
3	23	11
4	32	11
5	49	11
6	86	11
7	123	11
8	166	11
9	202	11
10	228	11
11	230	11