Details

analyze100.0ms (4.8%)

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%	74.9%	25.1%	4
18.7%	56.2%	25.1%	5
28.1%	34.3%	37.6%	6
34.3%	28.1%	37.6%	7
39%	17.2%	43.8%	8
41%	13.7%	45.4%	9
43.1%	8.4%	48.5%	10
44%	6.7%	49.3%	11
45%	4.1%	50.8%	12
45.4%	3.3%	51.2%	13
45.9%	2.1%	52%	14

Compiler

Compiled 11 to 8 computations (27.3% saved)

sample18.0ms (0.9%)

Algorithm

1×

intervals

Results

10.0ms	256×	body	128	valid
0.0ms	5×	body	128	nan
0.0ms	2×	body	128	invalid

Compiler

Compiled 23 to 17 computations (26.1% saved)

simplify17.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

151×	`fma-def_binary64`
131×	`fma-neg_binary64`
45×	`cancel-sign-sub-inv_binary64`
38×	`sub-neg_binary64`
31×	`unsub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	12
1	16	10
2	37	10
3	63	10
4	127	10
5	233	10
6	324	10
7	361	10
8	400	10
9	414	10
10	383	10

prune9.0ms (0.4%)

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
	0.1b	(fma.f64 y (sqrt.f64 x) (-.f64 1 x))
▶	0.1b	(+.f64 (-.f64 1 x) (*.f64 y (sqrt.f64 x)))

Compiler

Compiled 55 to 36 computations (34.5% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (-.f64 1 x) (*.f64 y (sqrt.f64 x)))
✓	0.3b	(*.f64 y (sqrt.f64 x))

series23.0ms (1.1%)

Counts

2 → 15

Calls

2 calls:

12.0ms	(+.f64 (-.f64 1 x) (*.f64 y (sqrt.f64 x)))
11.0ms	(*.f64 y (sqrt.f64 x))

rewrite13.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64`
16×	`*-un-lft-identity_binary64`
13×	`associate-+l+_binary64`
13×	`add-cube-cbrt_binary64`
9×	`prod-diff_binary64`

Counts

2 → 58

Calls

2 calls:

6.0ms	(+.f64 (-.f64 1 x) (*.f64 y (sqrt.f64 x)))
3.0ms	(*.f64 y (sqrt.f64 x))

simplify75.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

433×	`fma-neg_binary64`
391×	`times-frac_binary64`
347×	`fma-def_binary64`
321×	`associate-l_binary64`
256×	`distribute-rgt-in_binary64`

Counts

73 → 84

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	92	672
1	214	646
2	643	637
3	2361	637
4	4129	637
5	4926	637

prune74.0ms (3.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	79	5	84
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	79	7	86

Error

0.0b

Counts

86 → 7

Alt Table

Status	Error	Program
✓	0.1b	(+.f64 (-.f64 1 x) (*.f64 y (sqrt.f64 x)))
	0.2b	(+.f64 (-.f64 1 x) (.f64 (.f64 y (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (sqrt.f64 x))))
	17.1b	(+.f64 (-.f64 1 x) (cbrt.f64 (pow.f64 (*.f64 y (sqrt.f64 x)) 3)))
	23.4b	(/.f64 (-.f64 (.f64 (-.f64 1 x) (-.f64 1 x)) (.f64 (.f64 y (sqrt.f64 x)) (.f64 y (sqrt.f64 x)))) (-.f64 (-.f64 1 x) (*.f64 y (sqrt.f64 x))))
▶	0.1b	(fma.f64 y (sqrt.f64 x) (-.f64 1 x))
	0.3b	(+.f64 (-.f64 1 x) (.f64 (.f64 y (fabs.f64 (cbrt.f64 x))) (sqrt.f64 (cbrt.f64 x))))
	0.4b	(+.f64 (-.f64 1 x) (.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (*.f64 (cbrt.f64 y) (sqrt.f64 x))))

Compiler

Compiled 1473 to 680 computations (53.8% saved)

localize5.0ms (0.2%)

Local error

Found 1 expressions with local error:

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

series8.0ms (0.4%)

Counts

1 → 15

Calls

1 calls:

8.0ms

(fma.f64 y (sqrt.f64 x) (-.f64 1 x))

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

1×	`*-un-lft-identity_binary64`
1×	`add-sqr-sqrt_binary64`
1×	`add-cube-cbrt_binary64`
1×	`add-cbrt-cube_binary64`
1×	`add-exp-log_binary64`

Counts

1 → 10

Calls

1 calls:

0.0ms

(fma.f64 y (sqrt.f64 x) (-.f64 1 x))

simplify58.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

709×	`distribute-rgt-in_binary64`
693×	`distribute-lft-in_binary64`
571×	`neg-mul-1_binary64`
544×	`unsub-neg_binary64`
296×	`associate-+l+_binary64`

Counts

25 → 25

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	23	263
1	34	241
2	94	241
3	413	241
4	2431	241
5	4317	241
6	4957	241

prune23.0ms (1.1%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	25	0	25
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	25	7	32

Error

0.0b

Counts

32 → 7

Alt Table

Status	Error	Program
✓	0.1b	(+.f64 (-.f64 1 x) (*.f64 y (sqrt.f64 x)))
▶	0.2b	(+.f64 (-.f64 1 x) (.f64 (.f64 y (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (sqrt.f64 x))))
	17.1b	(+.f64 (-.f64 1 x) (cbrt.f64 (pow.f64 (*.f64 y (sqrt.f64 x)) 3)))
	23.4b	(/.f64 (-.f64 (.f64 (-.f64 1 x) (-.f64 1 x)) (.f64 (.f64 y (sqrt.f64 x)) (.f64 y (sqrt.f64 x)))) (-.f64 (-.f64 1 x) (*.f64 y (sqrt.f64 x))))
✓	0.1b	(fma.f64 y (sqrt.f64 x) (-.f64 1 x))
	0.3b	(+.f64 (-.f64 1 x) (.f64 (.f64 y (fabs.f64 (cbrt.f64 x))) (sqrt.f64 (cbrt.f64 x))))
	0.4b	(+.f64 (-.f64 1 x) (.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (*.f64 (cbrt.f64 y) (sqrt.f64 x))))

Compiler

Compiled 450 to 255 computations (43.3% saved)

localize7.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

series267.0ms (12.9%)

Counts

4 → 55

Calls

4 calls:

229.0ms	(*.f64 y (sqrt.f64 (sqrt.f64 x)))
17.0ms	(sqrt.f64 (sqrt.f64 x))
11.0ms	(.f64 (.f64 y (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (sqrt.f64 x)))
9.0ms	(+.f64 (-.f64 1 x) (.f64 (.f64 y (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (sqrt.f64 x))))

rewrite27.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`add-sqr-sqrt_binary64`
31×	`sqrt-prod_binary64`
24×	`*-un-lft-identity_binary64`
21×	`add-cube-cbrt_binary64`
18×	`associate-r_binary64`

Counts

4 → 109

Calls

4 calls:

7.0ms	(+.f64 (-.f64 1 x) (.f64 (.f64 y (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (sqrt.f64 x))))
7.0ms	(.f64 (.f64 y (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (sqrt.f64 x)))
4.0ms	(*.f64 y (sqrt.f64 (sqrt.f64 x)))
1.0ms	(sqrt.f64 (sqrt.f64 x))

simplify100.0ms (4.8%)

Algorithm

1×	egg-herbie

Rules

500×	`times-frac_binary64`
485×	`fma-neg_binary64`
437×	`fma-def_binary64`
287×	`distribute-rgt-in_binary64`
268×	`distribute-lft-in_binary64`

Counts

164 → 146

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	132	1445
1	297	1396
2	938	1387
3	2579	1387
4	4265	1387
5	5337	1387

prune163.0ms (7.9%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	163	5	168
Fresh	3	1	4
Picked	1	0	1
Done	1	1	2
Total	168	7	175

Error

Counts

175 → 7

Alt Table

Status	Error	Program
▶	0.2b	(+.f64 (-.f64 1 x) (.f64 (.f64 y (sqrt.f64 (sqrt.f64 x))) (pow.f64 x 1/4)))
✓	0.1b	(fma.f64 y (sqrt.f64 x) (-.f64 1 x))
	0.4b	(+.f64 (-.f64 1 x) (.f64 (.f64 (*.f64 y (sqrt.f64 (sqrt.f64 x))) (fabs.f64 (cbrt.f64 (sqrt.f64 x)))) (sqrt.f64 (cbrt.f64 (sqrt.f64 x)))))
	0.3b	(+.f64 (-.f64 1 x) (.f64 (.f64 (*.f64 y (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (sqrt.f64 (sqrt.f64 x)))) (sqrt.f64 (sqrt.f64 (sqrt.f64 x)))))
	0.2b	(+.f64 (-.f64 1 x) (.f64 y (.f64 (sqrt.f64 (sqrt.f64 x)) (sqrt.f64 (sqrt.f64 x)))))
	0.3b	(+.f64 (-.f64 1 x) (.f64 (.f64 y (fabs.f64 (cbrt.f64 x))) (sqrt.f64 (cbrt.f64 x))))
	0.4b	(+.f64 (-.f64 1 x) (.f64 (.f64 (.f64 (cbrt.f64 (.f64 y (sqrt.f64 (sqrt.f64 x)))) (cbrt.f64 (.f64 y (sqrt.f64 (sqrt.f64 x))))) (cbrt.f64 (.f64 y (sqrt.f64 (sqrt.f64 x))))) (sqrt.f64 (sqrt.f64 x))))

Compiler

Compiled 3328 to 1220 computations (63.3% saved)

localize10.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (-.f64 1 x) (.f64 (.f64 y (sqrt.f64 (sqrt.f64 x))) (pow.f64 x 1/4)))
	0.1b	(sqrt.f64 (sqrt.f64 x))
	0.3b	(*.f64 y (sqrt.f64 (sqrt.f64 x)))
✓	0.3b	(.f64 (.f64 y (sqrt.f64 (sqrt.f64 x))) (pow.f64 x 1/4))

series27.0ms (1.3%)

Counts

2 → 27

Calls

2 calls:

15.0ms	(.f64 (.f64 y (sqrt.f64 (sqrt.f64 x))) (pow.f64 x 1/4))
12.0ms	(+.f64 (-.f64 1 x) (.f64 (.f64 y (sqrt.f64 (sqrt.f64 x))) (pow.f64 x 1/4)))

rewrite19.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`*-un-lft-identity_binary64`
15×	`add-sqr-sqrt_binary64`
15×	`add-exp-log_binary64`
13×	`associate-+l+_binary64`
12×	`add-cube-cbrt_binary64`

Counts

2 → 60

Calls

2 calls:

7.0ms	(+.f64 (-.f64 1 x) (.f64 (.f64 y (sqrt.f64 (sqrt.f64 x))) (pow.f64 x 1/4)))
6.0ms	(.f64 (.f64 y (sqrt.f64 (sqrt.f64 x))) (pow.f64 x 1/4))

simplify80.0ms (3.9%)

Algorithm

1×	egg-herbie

Rules

930×	`fma-neg_binary64`
453×	`fma-def_binary64`
445×	`cancel-sign-sub-inv_binary64`
371×	`times-frac_binary64`
323×	`exp-prod_binary64`

Counts

87 → 98

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	116	1168
1	283	1084
2	960	1069
3	2618	744
4	3645	743
5	5012	743

prune154.0ms (7.4%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	148	2	150
Fresh	2	3	5
Picked	0	1	1
Done	0	1	1
Total	150	7	157

Error

Counts

157 → 7

Alt Table

Status	Error	Program
✓	0.2b	(+.f64 (-.f64 1 x) (.f64 (.f64 y (sqrt.f64 (sqrt.f64 x))) (pow.f64 x 1/4)))
✓	0.1b	(fma.f64 y (sqrt.f64 x) (-.f64 1 x))
	0.4b	(+.f64 (-.f64 1 x) (.f64 (.f64 (*.f64 y (sqrt.f64 (sqrt.f64 x))) (fabs.f64 (cbrt.f64 (sqrt.f64 x)))) (sqrt.f64 (cbrt.f64 (sqrt.f64 x)))))
	0.3b	(+.f64 (-.f64 1 x) (.f64 (.f64 y (*.f64 (fabs.f64 (cbrt.f64 (sqrt.f64 x))) (sqrt.f64 (cbrt.f64 (sqrt.f64 x))))) (pow.f64 x 1/4)))
	0.3b	(+.f64 (-.f64 1 x) (.f64 (.f64 (*.f64 y (sqrt.f64 (sqrt.f64 x))) (pow.f64 (sqrt.f64 x) 1/4)) (pow.f64 (sqrt.f64 x) 1/4)))
	0.2b	(+.f64 (-.f64 1 x) (.f64 y (.f64 (sqrt.f64 (sqrt.f64 x)) (sqrt.f64 (sqrt.f64 x)))))
	0.3b	(+.f64 (-.f64 1 x) (.f64 (.f64 y (fabs.f64 (cbrt.f64 x))) (sqrt.f64 (cbrt.f64 x))))

Compiler

Compiled 2910 to 1460 computations (49.8% saved)

regimes136.0ms (6.6%)

Accuracy

Total 0.1b remaining (81.2%)

Threshold costs 0.1b (81.2%)

Counts

48 → 1

Compiler

Compiled 2336 to 1450 computations (37.9% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
2×	`sub-neg_binary64`
1×	`*-commutative_binary64`
1×	`neg-sub0_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	11	10
2	15	10
3	17	10
4	18	10
5	17	10

end0.0ms (0%)

Compiler: Compiled 9 to 6 computations (33.3% saved)

sample648.0ms (31.3%)

Algorithm

1×

intervals

Results

324.0ms	7999×	body	128	valid
5.0ms	135×	body	128	nan
3.0ms	78×	body	128	invalid
0.0ms	1×	body	1024	valid

Compiler

Compiled 139 to 93 computations (33.1% saved)

Iter	Nodes	Cost
0	8	12
1	16	10
2	37	10
3	63	10
4	127	10
5	233	10
6	324	10
7	361	10
8	400	10
9	414	10
10	383	10

Iter	Nodes	Cost
0	8	12
1	16	10
2	37	10
3	63	10
4	127	10
5	233	10
6	324	10
7	361	10
8	400	10
9	414	10
10	383	10

Details

analyze100.0ms (4.8%)

sample18.0ms (0.9%)

simplify17.0ms (0.8%)

prune9.0ms (0.4%)

localize5.0ms (0.2%)

series23.0ms (1.1%)

rewrite13.0ms (0.6%)

simplify75.0ms (3.6%)

prune74.0ms (3.6%)

localize5.0ms (0.2%)

series8.0ms (0.4%)

rewrite1.0ms (0%)

simplify58.0ms (2.8%)

prune23.0ms (1.1%)

localize7.0ms (0.3%)

series267.0ms (12.9%)

rewrite27.0ms (1.3%)

simplify100.0ms (4.8%)

prune163.0ms (7.9%)

localize10.0ms (0.5%)

series27.0ms (1.3%)

rewrite19.0ms (0.9%)

simplify80.0ms (3.9%)

prune154.0ms (7.4%)

regimes136.0ms (6.6%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample648.0ms (31.3%)

Profiling

Iter	Nodes	Cost
0	8	12
1	16	10
2	37	10
3	63	10
4	127	10
5	233	10
6	324	10
7	361	10
8	400	10
9	414	10
10	383	10