Details

analyze19.0ms (0.5%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
50%	50%	0.1%	2
50%	50%	0.1%	3
50%	25%	25.1%	4
50%	25%	25.1%	5
50%	12.5%	37.6%	6
50%	12.5%	37.6%	7
50%	6.2%	43.8%	8
50%	6.2%	43.8%	9
50%	3.1%	46.9%	10
50%	3.1%	46.9%	11
50%	1.6%	48.5%	12
50%	1.6%	48.5%	13
50%	0.8%	49.3%	14

Compiler

Compiled 11 to 8 computations (27.3% saved)

sample653.0ms (15.9%)

Results

586.0ms	8253×	body	128	valid
11.0ms	133×	body	128	invalid
0.0ms	1×	body	1024	valid
0.0ms	1×	body	512	valid
0.0ms	1×	body	256	valid

Compiler

Compiled 32 to 23 computations (28.1% saved)

simplify18.0ms (0.4%)

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

prune3.0ms (0.1%)

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

Compiler

Compiled 55 to 36 computations (34.5% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

series9.0ms (0.2%)

Counts

1 → 15

Calls

1 calls:

9.0ms

(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))

simplify54.0ms (1.3%)

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

prune20.0ms (0.5%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	21	4	25
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	23	4	27

Error

0.0b

Counts

27 → 4

Alt Table

Status	Error	Program
	33.9b	(*.f64 (sqrt.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x))) (sqrt.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x))))
	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))))
	25.0b	(cbrt.f64 (.f64 (.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x)) (fma.f64 y (sqrt.f64 x) (-.f64 1 x))) (fma.f64 y (sqrt.f64 x) (-.f64 1 x))))
▶	0.1b	(-.f64 (fma.f64 y (sqrt.f64 x) 1) x)

Compiler

Compiled 419 to 234 computations (44.2% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

series20.0ms (0.5%)

Counts

2 → 28

Calls

2 calls:

10.0ms	(-.f64 (fma.f64 y (sqrt.f64 x) 1) x)
10.0ms	(fma.f64 y (sqrt.f64 x) 1)

rewrite5.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`*-un-lft-identity_binary64`
12×	`add-sqr-sqrt_binary64`
10×	`add-cube-cbrt_binary64`
9×	`prod-diff_binary64`
4×	`add-log-exp_binary64`

Counts

2 → 41

Calls

2 calls:

3.0ms	(-.f64 (fma.f64 y (sqrt.f64 x) 1) x)
0.0ms	(fma.f64 y (sqrt.f64 x) 1)

simplify95.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

714×	`fma-neg_binary64`
379×	`*-commutative_binary64`
344×	`unswap-sqr_binary64`
279×	`associate-l_binary64`
264×	`fma-def_binary64`

Counts

69 → 59

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	74	729
1	126	688
2	425	655
3	1895	651
4	2826	651
5	4976	643
6	4974	643
7	4886	643

prune45.0ms (1.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	57	2	59
Fresh	2	1	3
Picked	0	1	1
Done	0	0	0
Total	59	4	63

Error

0.0b

Counts

63 → 4

Alt Table

Status	Error	Program
	25.0b	(cbrt.f64 (.f64 (.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x)) (fma.f64 y (sqrt.f64 x) (-.f64 1 x))) (fma.f64 y (sqrt.f64 x) (-.f64 1 x))))
	16.6b	(fma.f64 (sqrt.f64 (fma.f64 y (sqrt.f64 x) 1)) (sqrt.f64 (fma.f64 y (sqrt.f64 x) 1)) (neg.f64 x))
✓	0.1b	(-.f64 (fma.f64 y (sqrt.f64 x) 1) x)
▶	0.4b	(-.f64 (*.f64 (pow.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 x) 1)) 2) (cbrt.f64 (fma.f64 y (sqrt.f64 x) 1))) x)

Compiler

Compiled 1036 to 498 computations (51.9% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(fma.f64 y (sqrt.f64 x) 1)
✓	0.1b	(*.f64 (pow.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 x) 1)) 2) (cbrt.f64 (fma.f64 y (sqrt.f64 x) 1)))
✓	0.3b	(pow.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 x) 1)) 2)
✓	4.8b	(cbrt.f64 (fma.f64 y (sqrt.f64 x) 1))

series244.0ms (5.9%)

Counts

3 → 39

Calls

3 calls:

165.0ms	(pow.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 x) 1)) 2)
57.0ms	(cbrt.f64 (fma.f64 y (sqrt.f64 x) 1))
21.0ms	(*.f64 (pow.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 x) 1)) 2) (cbrt.f64 (fma.f64 y (sqrt.f64 x) 1)))

rewrite28.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`add-sqr-sqrt_binary64`
19×	`cbrt-prod_binary64`
16×	`unpow-prod-down_binary64`
12×	`*-un-lft-identity_binary64`
12×	`add-cube-cbrt_binary64`

Counts

3 → 82

Calls

3 calls:

12.0ms	(*.f64 (pow.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 x) 1)) 2) (cbrt.f64 (fma.f64 y (sqrt.f64 x) 1)))
4.0ms	(pow.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 x) 1)) 2)
1.0ms	(cbrt.f64 (fma.f64 y (sqrt.f64 x) 1))

simplify174.0ms (4.2%)

Algorithm

1×	egg-herbie

Rules

525×	`fma-def_binary64`
465×	`associate-l_binary64`
437×	`associate-r_binary64`
290×	`times-frac_binary64`
237×	`fma-neg_binary64`

Counts

121 → 159

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	182	2754
1	455	2613
2	1297	2485
3	4910	2485
4	5024	2485

prune623.0ms (15.1%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	225	7	232
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	226	10	236

Error

0.0b

Counts

236 → 10

Alt Table

Status	Error	Program
	25.0b	(cbrt.f64 (.f64 (.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x)) (fma.f64 y (sqrt.f64 x) (-.f64 1 x))) (fma.f64 y (sqrt.f64 x) (-.f64 1 x))))
	0.6b	(-.f64 (.f64 (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 x) 1))) 4) (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 x) 1))) 2)) (cbrt.f64 (fma.f64 y (sqrt.f64 x) 1))) x)
▶	0.4b	(-.f64 (.f64 (pow.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 x) 1)) 2) (cbrt.f64 (.f64 (pow.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 x) 1)) 2) (cbrt.f64 (fma.f64 y (sqrt.f64 x) 1))))) x)
	0.5b	(-.f64 (.f64 (.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 x) 1)) 2)) (cbrt.f64 (pow.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 x) 1)) 2))) (*.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 x) 1)) 2)) (cbrt.f64 (fma.f64 y (sqrt.f64 x) 1)))) x)
	0.4b	(-.f64 (pow.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 x) 1)) 3) x)
	16.7b	(-.f64 (.f64 (pow.f64 (.f64 (cbrt.f64 (sqrt.f64 (fma.f64 y (sqrt.f64 x) 1))) (cbrt.f64 (sqrt.f64 (fma.f64 y (sqrt.f64 x) 1)))) 2) (cbrt.f64 (fma.f64 y (sqrt.f64 x) 1))) x)
	16.7b	(-.f64 (.f64 (pow.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 x) 1)) 2) (.f64 (cbrt.f64 (sqrt.f64 (fma.f64 y (sqrt.f64 x) 1))) (cbrt.f64 (sqrt.f64 (fma.f64 y (sqrt.f64 x) 1))))) x)
	0.5b	(-.f64 (.f64 (pow.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 x) 1)) 2) (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 x) 1))) 2) (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 x) 1))))) x)
✓	0.1b	(-.f64 (fma.f64 y (sqrt.f64 x) 1) x)
✓	0.4b	(-.f64 (*.f64 (pow.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 x) 1)) 2) (cbrt.f64 (fma.f64 y (sqrt.f64 x) 1))) x)

Compiler

Compiled 7342 to 4516 computations (38.5% saved)

localize21.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (pow.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 x) 1)) 2) (cbrt.f64 (.f64 (pow.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 x) 1)) 2) (cbrt.f64 (fma.f64 y (sqrt.f64 x) 1)))))
	0.3b	(pow.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 x) 1)) 2)
✓	4.8b	(cbrt.f64 (*.f64 (pow.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 x) 1)) 2) (cbrt.f64 (fma.f64 y (sqrt.f64 x) 1))))
	4.8b	(cbrt.f64 (fma.f64 y (sqrt.f64 x) 1))

series126.0ms (3.1%)

Counts

2 → 26

Calls

2 calls:

103.0ms

(cbrt.f64 (*.f64 (pow.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 x) 1)) 2) (cbrt.f64 (fma.f64 y (sqrt.f64 x) 1))))

23.0ms

(*.f64 (pow.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 x) 1)) 2) (cbrt.f64 (*.f64 (pow.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 x) 1)) 2) (cbrt.f64 (fma.f64 y (sqrt.f64 x) 1)))))

rewrite24.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64`
11×	`associate-l_binary64`
8×	`unpow-prod-down_binary64`
7×	`add-exp-log_binary64`
6×	`*-un-lft-identity_binary64`

Counts

2 → 46

Calls

2 calls:

11.0ms

(*.f64 (pow.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 x) 1)) 2) (cbrt.f64 (*.f64 (pow.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 x) 1)) 2) (cbrt.f64 (fma.f64 y (sqrt.f64 x) 1)))))

6.0ms

(cbrt.f64 (*.f64 (pow.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 x) 1)) 2) (cbrt.f64 (fma.f64 y (sqrt.f64 x) 1))))

simplify123.0ms (3%)

Algorithm

1×	egg-herbie

Rules

699×	`associate-/l*_binary64`
291×	`cancel-sign-sub-inv_binary64`
269×	`associate-l_binary64`
240×	`associate-r_binary64`
233×	`fma-def_binary64`

Counts

72 → 100

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	129	2266
1	310	1313
2	760	1271
3	2519	1094
4	5137	1094

prune1.1s (27%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	321	0	321
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	321	10	331

Error

0.0b

Counts

331 → 10

Alt Table

Status	Error	Program
	25.0b	(cbrt.f64 (.f64 (.f64 (fma.f64 y (sqrt.f64 x) (-.f64 1 x)) (fma.f64 y (sqrt.f64 x) (-.f64 1 x))) (fma.f64 y (sqrt.f64 x) (-.f64 1 x))))
	0.6b	(-.f64 (.f64 (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 x) 1))) 4) (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 x) 1))) 2)) (cbrt.f64 (fma.f64 y (sqrt.f64 x) 1))) x)
✓	0.4b	(-.f64 (.f64 (pow.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 x) 1)) 2) (cbrt.f64 (.f64 (pow.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 x) 1)) 2) (cbrt.f64 (fma.f64 y (sqrt.f64 x) 1))))) x)
	0.5b	(-.f64 (.f64 (.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 x) 1)) 2)) (cbrt.f64 (pow.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 x) 1)) 2))) (*.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 x) 1)) 2)) (cbrt.f64 (fma.f64 y (sqrt.f64 x) 1)))) x)
	0.4b	(-.f64 (pow.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 x) 1)) 3) x)
	16.7b	(-.f64 (.f64 (pow.f64 (.f64 (cbrt.f64 (sqrt.f64 (fma.f64 y (sqrt.f64 x) 1))) (cbrt.f64 (sqrt.f64 (fma.f64 y (sqrt.f64 x) 1)))) 2) (cbrt.f64 (fma.f64 y (sqrt.f64 x) 1))) x)
	16.7b	(-.f64 (.f64 (pow.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 x) 1)) 2) (.f64 (cbrt.f64 (sqrt.f64 (fma.f64 y (sqrt.f64 x) 1))) (cbrt.f64 (sqrt.f64 (fma.f64 y (sqrt.f64 x) 1))))) x)
	0.5b	(-.f64 (.f64 (pow.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 x) 1)) 2) (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 x) 1))) 2) (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 x) 1))))) x)
✓	0.1b	(-.f64 (fma.f64 y (sqrt.f64 x) 1) x)
✓	0.4b	(-.f64 (*.f64 (pow.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 x) 1)) 2) (cbrt.f64 (fma.f64 y (sqrt.f64 x) 1))) x)

Compiler

Compiled 13393 to 8456 computations (36.9% saved)

regimes250.0ms (6.1%)

Accuracy

Total 0.0b remaining (50%)

Threshold costs 0.0b (50%)

Counts

36 → 1

Compiler

Compiled 2204 to 1420 computations (35.6% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	12
1	14	12
2	18	12
3	20	12
4	21	12
5	20	12

end427.0ms (10.4%)

Compiler: Compiled 271 to 185 computations (31.7% 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

analyze19.0ms (0.5%)

sample653.0ms (15.9%)

simplify18.0ms (0.4%)

prune3.0ms (0.1%)

localize5.0ms (0.1%)

series9.0ms (0.2%)

rewrite1.0ms (0%)

simplify54.0ms (1.3%)

prune20.0ms (0.5%)

localize6.0ms (0.1%)

series20.0ms (0.5%)

rewrite5.0ms (0.1%)

simplify95.0ms (2.3%)

prune45.0ms (1.1%)

localize8.0ms (0.2%)

series244.0ms (5.9%)

rewrite28.0ms (0.7%)

simplify174.0ms (4.2%)

prune623.0ms (15.1%)

localize21.0ms (0.5%)

series126.0ms (3.1%)

rewrite24.0ms (0.6%)

simplify123.0ms (3%)

prune1.1s (27%)

regimes250.0ms (6.1%)

simplify3.0ms (0.1%)

end427.0ms (10.4%)

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