Details

analyze71.0ms (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%	74.9%	25.1%	4
12.5%	62.4%	25.1%	5
25%	37.5%	37.6%	6
31.2%	31.2%	37.6%	7
37.5%	18.7%	43.8%	8
39%	15.6%	45.4%	9
42.1%	9.4%	48.5%	10
42.9%	7.8%	49.3%	11
44.5%	4.7%	50.8%	12
44.9%	3.9%	51.2%	13
45.7%	2.3%	52%	14

Compiler

Compiled 11 to 8 computations (27.3% saved)

sample853.0ms (36.4%)

Results

784.0ms	8253×	body	128	valid
19.0ms	189×	body	128	invalid
1.0ms	3×	body	1024	valid

Compiler

Compiled 32 to 23 computations (28.1% saved)

simplify17.0ms (0.7%)

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

prune4.0ms (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
▶	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 1 expressions with local error:

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

series6.0ms (0.3%)

Counts

1 → 15

Calls

1 calls:

6.0ms

(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))

simplify51.0ms (2.2%)

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

prune17.0ms (0.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	23	2	25
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	23	4	27

Error

0.1b

Counts

27 → 4

Alt Table

Status	Error	Program
	0.9b	(.f64 (.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x))) (cbrt.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x)))) (cbrt.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x))))
	30.9b	(cbrt.f64 (pow.f64 (-.f64 (fma.f64 y (sqrt.f64 x) 1) x) 3))
✓	0.1b	(fma.f64 y (sqrt.f64 x) (-.f64 1 x))
▶	0.1b	(+.f64 (-.f64 1 x) (*.f64 y (sqrt.f64 x)))

Compiler

Compiled 364 to 206 computations (43.4% 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))

series16.0ms (0.7%)

Counts

2 → 15

Calls

2 calls:

9.0ms	(*.f64 y (sqrt.f64 x))
7.0ms	(+.f64 (-.f64 1 x) (*.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:

7.0ms	(+.f64 (-.f64 1 x) (*.f64 y (sqrt.f64 x)))
3.0ms	(*.f64 y (sqrt.f64 x))

simplify69.0ms (2.9%)

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

prune70.0ms (3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	80	4	84
Fresh	2	0	2
Picked	1	0	1
Done	0	1	1
Total	83	5	88

Error

0.0b

Counts

88 → 5

Alt Table

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

Compiler

Compiled 1422 to 637 computations (55.2% 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)))

series221.0ms (9.5%)

Counts

4 → 55

Calls

4 calls:

183.0ms	(*.f64 y (sqrt.f64 (sqrt.f64 x)))
20.0ms	(sqrt.f64 (sqrt.f64 x))
12.0ms	(.f64 (.f64 y (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (sqrt.f64 x)))
7.0ms	(+.f64 (-.f64 1 x) (.f64 (.f64 y (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (sqrt.f64 x))))

rewrite25.0ms (1.1%)

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:

6.0ms	(+.f64 (-.f64 1 x) (.f64 (.f64 y (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (sqrt.f64 x))))
6.0ms	(.f64 (.f64 y (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (sqrt.f64 x)))
5.0ms	(*.f64 y (sqrt.f64 (sqrt.f64 x)))
1.0ms	(sqrt.f64 (sqrt.f64 x))

simplify95.0ms (4%)

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

prune135.0ms (5.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	165	3	168
Fresh	2	1	3
Picked	1	0	1
Done	0	1	1
Total	168	5	173

Error

0.0b

Counts

173 → 5

Alt Table

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

Compiler

Compiled 3238 to 1182 computations (63.5% saved)

localize11.0ms (0.5%)

Local error

Found 4 expressions with local error:

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

series195.0ms (8.3%)

Counts

3 → 31

Calls

3 calls:

176.0ms	(*.f64 y (pow.f64 x 1/4))
10.0ms	(.f64 (.f64 y (pow.f64 x 1/4)) (sqrt.f64 (sqrt.f64 x)))
9.0ms	(+.f64 (-.f64 1 x) (.f64 (.f64 y (pow.f64 x 1/4)) (sqrt.f64 (sqrt.f64 x))))

rewrite25.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`add-sqr-sqrt_binary64`
20×	`*-un-lft-identity_binary64`
18×	`add-exp-log_binary64`
17×	`add-cube-cbrt_binary64`
16×	`associate-r_binary64`

Counts

3 → 88

Calls

3 calls:

8.0ms	(+.f64 (-.f64 1 x) (.f64 (.f64 y (pow.f64 x 1/4)) (sqrt.f64 (sqrt.f64 x))))
7.0ms	(.f64 (.f64 y (pow.f64 x 1/4)) (sqrt.f64 (sqrt.f64 x)))
4.0ms	(*.f64 y (pow.f64 x 1/4))

simplify87.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

948×	`fma-neg_binary64`
453×	`fma-def_binary64`
433×	`cancel-sign-sub-inv_binary64`
335×	`*-commutative_binary64`
331×	`exp-prod_binary64`

Counts

119 → 131

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	150	1582
1	337	1480
2	1110	1393
3	2849	1045
4	3704	1044
5	4940	1044

prune125.0ms (5.4%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	153	0	153
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	153	5	158

Error

0.0b

Counts

158 → 5

Alt Table

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

Compiler

Compiled 2933 to 1576 computations (46.3% saved)

regimes137.0ms (5.9%)

Accuracy

Total 0.1b remaining (75.7%)

Threshold costs 0.1b (75.7%)

Counts

50 → 1

Compiler

Compiled 2171 to 1501 computations (30.9% saved)

simplify2.0ms (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

end78.0ms (3.3%)

Compiler: Compiled 99 to 65 computations (34.3% 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

analyze71.0ms (3%)

sample853.0ms (36.4%)

simplify17.0ms (0.7%)

prune4.0ms (0.2%)

localize5.0ms (0.2%)

series6.0ms (0.3%)

rewrite1.0ms (0%)

simplify51.0ms (2.2%)

prune17.0ms (0.7%)

localize5.0ms (0.2%)

series16.0ms (0.7%)

rewrite13.0ms (0.6%)

simplify69.0ms (2.9%)

prune70.0ms (3%)

localize7.0ms (0.3%)

series221.0ms (9.5%)

rewrite25.0ms (1.1%)

simplify95.0ms (4%)

prune135.0ms (5.8%)

localize11.0ms (0.5%)

series195.0ms (8.3%)

rewrite25.0ms (1%)

simplify87.0ms (3.7%)

prune125.0ms (5.4%)

regimes137.0ms (5.9%)

simplify2.0ms (0.1%)

end78.0ms (3.3%)

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