Details

analyze360.0ms (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%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
12.5%	87.4%	0.1%	7
31.2%	68.6%	0.1%	8
37.4%	59.3%	3.3%	9
45.2%	48.4%	6.4%	10
56.9%	36.7%	6.4%	11
60.5%	30.8%	8.7%	12
64.2%	24.8%	11.1%	13
70.3%	18.6%	11.1%	14

Compiler

Compiled 11 to 8 computations (27.3% saved)

sample992.0ms (22.1%)

Symmetry

(sort y z)

Results

875.0ms	8256×	body	128	valid
52.0ms	544×	body	128	invalid

Compiler

Compiled 32 to 23 computations (28.1% saved)

simplify24.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

419×	`fma-def_binary64`
121×	`fma-neg_binary64`
46×	`distribute-rgt-in_binary64`
45×	`associate-r_binary64`
43×	`associate-l_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	10
1	17	10
2	32	10
3	73	10
4	175	10
5	216	10
6	290	10
7	411	10
8	431	10
9	481	10
10	484	10
11	504	10
12	453	10

prune2.0ms (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

3.6b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	3.6b	(.f64 x (-.f64 1 (.f64 y z)))

Compiler

Compiled 30 to 21 computations (30% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	3.4b	(.f64 x (-.f64 1 (.f64 y z)))

series9.0ms (0.2%)

Counts

1 → 36

Calls

1 calls:

9.0ms

(*.f64 x (-.f64 1 (*.f64 y z)))

rewrite8.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`add-sqr-sqrt_binary64`
6×	`prod-diff_binary64`
5×	`distribute-lft-in_binary64`
5×	`distribute-rgt-in_binary64`
5×	`*-un-lft-identity_binary64`

Counts

1 → 32

Calls

1 calls:

5.0ms

(*.f64 x (-.f64 1 (*.f64 y z)))

simplify53.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

811×	`fma-def_binary64`
608×	`distribute-neg-out_binary64`
586×	`unsub-neg_binary64`
290×	`associate-l_binary64`
267×	`*-commutative_binary64`

Counts

68 → 50

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	70	843
1	139	783
2	446	747
3	1293	729
4	2542	729
5	4900	729

prune42.0ms (0.9%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	42	8	50
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	43	8	51

Error

0.0b

Counts

51 → 8

Alt Table

Status	Error	Program
	15.4b	(.f64 (.f64 x (sqrt.f64 (-.f64 1 (.f64 y z)))) (sqrt.f64 (-.f64 1 (.f64 y z))))
	32.8b	(.f64 (sqrt.f64 (.f64 x (-.f64 1 (.f64 y z)))) (sqrt.f64 (.f64 x (-.f64 1 (*.f64 y z)))))
	4.4b	(-.f64 x (.f64 y (.f64 z x)))
	4.8b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (cbrt.f64 x) (-.f64 1 (.f64 y z))))
	16.6b	(/.f64 (.f64 x (-.f64 1 (.f64 (.f64 y z) (.f64 y z)))) (+.f64 1 (*.f64 y z)))
▶	3.6b	(+.f64 (.f64 1 x) (.f64 (neg.f64 (*.f64 y z)) x))
	4.0b	(.f64 (.f64 x (.f64 (cbrt.f64 (-.f64 1 (.f64 y z))) (cbrt.f64 (-.f64 1 (.f64 y z))))) (cbrt.f64 (-.f64 1 (.f64 y z))))
	4.8b	(.f64 (.f64 (cbrt.f64 (.f64 x (-.f64 1 (.f64 y z)))) (cbrt.f64 (.f64 x (-.f64 1 (.f64 y z))))) (cbrt.f64 (.f64 x (-.f64 1 (.f64 y z)))))

Compiler

Compiled 996 to 519 computations (47.9% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 1 x) (.f64 (neg.f64 (*.f64 y z)) x))
✓	7.3b	(.f64 (neg.f64 (.f64 y z)) x)

series20.0ms (0.4%)

Counts

2 → 72

Calls

2 calls:

11.0ms	(.f64 (neg.f64 (.f64 y z)) x)
8.0ms	(+.f64 (.f64 1 x) (.f64 (neg.f64 (*.f64 y z)) x))

rewrite7.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`associate-l_binary64`
6×	`add-sqr-sqrt_binary64`
4×	`*-un-lft-identity_binary64`
4×	`add-cube-cbrt_binary64`
4×	`add-cbrt-cube_binary64`

Counts

2 → 40

Calls

2 calls:

3.0ms	(.f64 (neg.f64 (.f64 y z)) x)
2.0ms	(+.f64 (.f64 1 x) (.f64 (neg.f64 (*.f64 y z)) x))

simplify82.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

794×	`unsub-neg_binary64`
448×	`neg-sub0_binary64`
446×	`fma-neg_binary64`
427×	`neg-mul-1_binary64`
370×	`distribute-rgt-neg-in_binary64`

Counts

112 → 67

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	73	1161
1	204	1137
2	859	1127
3	2574	1126
4	4048	1126
5	5032	1126

prune54.0ms (1.2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	67	0	67
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	67	8	75

Error

0.0b

Counts

75 → 8

Alt Table

Status	Error	Program
	15.4b	(.f64 (.f64 x (sqrt.f64 (-.f64 1 (.f64 y z)))) (sqrt.f64 (-.f64 1 (.f64 y z))))
	32.8b	(.f64 (sqrt.f64 (.f64 x (-.f64 1 (.f64 y z)))) (sqrt.f64 (.f64 x (-.f64 1 (*.f64 y z)))))
	4.4b	(-.f64 x (.f64 y (.f64 z x)))
	4.8b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (cbrt.f64 x) (-.f64 1 (.f64 y z))))
	16.6b	(/.f64 (.f64 x (-.f64 1 (.f64 (.f64 y z) (.f64 y z)))) (+.f64 1 (*.f64 y z)))
✓	3.6b	(+.f64 (.f64 1 x) (.f64 (neg.f64 (*.f64 y z)) x))
▶	4.0b	(.f64 (.f64 x (.f64 (cbrt.f64 (-.f64 1 (.f64 y z))) (cbrt.f64 (-.f64 1 (.f64 y z))))) (cbrt.f64 (-.f64 1 (.f64 y z))))
	4.8b	(.f64 (.f64 (cbrt.f64 (.f64 x (-.f64 1 (.f64 y z)))) (cbrt.f64 (.f64 x (-.f64 1 (.f64 y z))))) (cbrt.f64 (.f64 x (-.f64 1 (.f64 y z)))))

Compiler

Compiled 1299 to 545 computations (58% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (.f64 x (.f64 (cbrt.f64 (-.f64 1 (.f64 y z))) (cbrt.f64 (-.f64 1 (.f64 y z))))) (cbrt.f64 (-.f64 1 (.f64 y z))))
✓	0.2b	(.f64 (cbrt.f64 (-.f64 1 (.f64 y z))) (cbrt.f64 (-.f64 1 (*.f64 y z))))
✓	1.1b	(.f64 x (.f64 (cbrt.f64 (-.f64 1 (.f64 y z))) (cbrt.f64 (-.f64 1 (.f64 y z)))))
✓	3.5b	(cbrt.f64 (-.f64 1 (*.f64 y z)))

series516.0ms (11.5%)

Counts

4 → 120

Calls

4 calls:

462.0ms	(.f64 x (.f64 (cbrt.f64 (-.f64 1 (.f64 y z))) (cbrt.f64 (-.f64 1 (.f64 y z)))))
22.0ms	(cbrt.f64 (-.f64 1 (*.f64 y z)))
21.0ms	(.f64 (cbrt.f64 (-.f64 1 (.f64 y z))) (cbrt.f64 (-.f64 1 (*.f64 y z))))
11.0ms	(.f64 (.f64 x (.f64 (cbrt.f64 (-.f64 1 (.f64 y z))) (cbrt.f64 (-.f64 1 (.f64 y z))))) (cbrt.f64 (-.f64 1 (.f64 y z))))

rewrite47.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

80×	`cbrt-div_binary64`
44×	`associate-*r/_binary64`
40×	`flip--_binary64`
40×	`flip3--_binary64`
36×	`frac-times_binary64`

Counts

4 → 146

Calls

4 calls:

12.0ms	(.f64 (.f64 x (.f64 (cbrt.f64 (-.f64 1 (.f64 y z))) (cbrt.f64 (-.f64 1 (.f64 y z))))) (cbrt.f64 (-.f64 1 (.f64 y z))))
7.0ms	(.f64 x (.f64 (cbrt.f64 (-.f64 1 (.f64 y z))) (cbrt.f64 (-.f64 1 (.f64 y z)))))
7.0ms	(.f64 (cbrt.f64 (-.f64 1 (.f64 y z))) (cbrt.f64 (-.f64 1 (*.f64 y z))))
2.0ms	(cbrt.f64 (-.f64 1 (*.f64 y z)))

simplify250.0ms (5.6%)

Algorithm

1×	egg-herbie

Rules

440×	`associate-/r*_binary64`
405×	`associate-l_binary64`
371×	`associate-r_binary64`
320×	`times-frac_binary64`
306×	`fma-neg_binary64`

Counts

266 → 321

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	404	8821
1	1193	7992
2	4366	7552
3	4988	7512
4	4996	7512
5	5017	7512

prune475.0ms (10.6%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	433	2	435
Fresh	2	4	6
Picked	0	1	1
Done	0	1	1
Total	435	8	443

Error

0.0b

Counts

443 → 8

Alt Table

Status	Error	Program
	15.4b	(.f64 (.f64 x (sqrt.f64 (-.f64 1 (.f64 y z)))) (sqrt.f64 (-.f64 1 (.f64 y z))))
	4.4b	(-.f64 x (.f64 y (.f64 z x)))
	4.8b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (cbrt.f64 x) (-.f64 1 (.f64 y z))))
▶	4.0b	(.f64 (.f64 (.f64 x (.f64 (cbrt.f64 (-.f64 1 (.f64 y z))) (cbrt.f64 (-.f64 1 (.f64 y z))))) (cbrt.f64 (.f64 (cbrt.f64 (-.f64 1 (.f64 y z))) (cbrt.f64 (-.f64 1 (.f64 y z)))))) (cbrt.f64 (cbrt.f64 (-.f64 1 (.f64 y z)))))
	16.6b	(/.f64 (.f64 x (-.f64 1 (.f64 (.f64 y z) (.f64 y z)))) (fma.f64 y z 1))
✓	3.6b	(+.f64 (.f64 1 x) (.f64 (neg.f64 (*.f64 y z)) x))
✓	4.0b	(.f64 (.f64 x (.f64 (cbrt.f64 (-.f64 1 (.f64 y z))) (cbrt.f64 (-.f64 1 (.f64 y z))))) (cbrt.f64 (-.f64 1 (.f64 y z))))
	4.8b	(.f64 (.f64 (cbrt.f64 (.f64 x (-.f64 1 (.f64 y z)))) (cbrt.f64 (.f64 x (-.f64 1 (.f64 y z))))) (cbrt.f64 (.f64 x (-.f64 1 (.f64 y z)))))

Compiler

Compiled 17940 to 10439 computations (41.8% saved)

localize14.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(cbrt.f64 (cbrt.f64 (-.f64 1 (*.f64 y z))))
	1.1b	(.f64 x (.f64 (cbrt.f64 (-.f64 1 (.f64 y z))) (cbrt.f64 (-.f64 1 (.f64 y z)))))
✓	1.2b	(cbrt.f64 (.f64 (cbrt.f64 (-.f64 1 (.f64 y z))) (cbrt.f64 (-.f64 1 (*.f64 y z)))))
	3.5b	(cbrt.f64 (-.f64 1 (*.f64 y z)))

series40.0ms (0.9%)

Counts

2 → 48

Calls

2 calls:

24.0ms	(cbrt.f64 (.f64 (cbrt.f64 (-.f64 1 (.f64 y z))) (cbrt.f64 (-.f64 1 (*.f64 y z)))))
16.0ms	(cbrt.f64 (cbrt.f64 (-.f64 1 (*.f64 y z))))

rewrite10.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`cbrt-div_binary64`
10×	`cbrt-prod_binary64`
7×	`flip--_binary64`
7×	`flip3--_binary64`
4×	`*-un-lft-identity_binary64`

Counts

2 → 37

Calls

2 calls:

5.0ms	(cbrt.f64 (.f64 (cbrt.f64 (-.f64 1 (.f64 y z))) (cbrt.f64 (-.f64 1 (*.f64 y z)))))
2.0ms	(cbrt.f64 (cbrt.f64 (-.f64 1 (*.f64 y z))))

simplify89.0ms (2%)

Algorithm

1×	egg-herbie

Rules

923×	`fma-def_binary64`
728×	`cancel-sign-sub-inv_binary64`
288×	`associate-/r*_binary64`
244×	`distribute-neg-frac_binary64`
184×	`sub-neg_binary64`

Counts

85 → 124

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	248	3406
1	676	3184
2	2335	3074
3	4989	3074

prune619.0ms (13.8%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	489	0	489
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	489	8	497

Error

0.0b

Counts

497 → 8

Alt Table

Status	Error	Program
	15.4b	(.f64 (.f64 x (sqrt.f64 (-.f64 1 (.f64 y z)))) (sqrt.f64 (-.f64 1 (.f64 y z))))
	4.4b	(-.f64 x (.f64 y (.f64 z x)))
	4.8b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (cbrt.f64 x) (-.f64 1 (.f64 y z))))
✓	4.0b	(.f64 (.f64 (.f64 x (.f64 (cbrt.f64 (-.f64 1 (.f64 y z))) (cbrt.f64 (-.f64 1 (.f64 y z))))) (cbrt.f64 (.f64 (cbrt.f64 (-.f64 1 (.f64 y z))) (cbrt.f64 (-.f64 1 (.f64 y z)))))) (cbrt.f64 (cbrt.f64 (-.f64 1 (.f64 y z)))))
	16.6b	(/.f64 (.f64 x (-.f64 1 (.f64 (.f64 y z) (.f64 y z)))) (fma.f64 y z 1))
✓	3.6b	(+.f64 (.f64 1 x) (.f64 (neg.f64 (*.f64 y z)) x))
✓	4.0b	(.f64 (.f64 x (.f64 (cbrt.f64 (-.f64 1 (.f64 y z))) (cbrt.f64 (-.f64 1 (.f64 y z))))) (cbrt.f64 (-.f64 1 (.f64 y z))))
	4.8b	(.f64 (.f64 (cbrt.f64 (.f64 x (-.f64 1 (.f64 y z)))) (cbrt.f64 (.f64 x (-.f64 1 (.f64 y z))))) (cbrt.f64 (.f64 x (-.f64 1 (.f64 y z)))))

Compiler

Compiled 28730 to 17028 computations (40.7% saved)

regimes496.0ms (11.1%)

Accuracy

Total 0.1b remaining (75.5%)

Threshold costs 0.1b (75.5%)

Counts

47 → 3

Compiler

Compiled 7387 to 4887 computations (33.8% saved)

bsearch2.0ms (0%)

Compiler: Compiled 6 to 4 computations (33.3% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

11×	`*-commutative_binary64`
7×	`+-commutative_binary64`
6×	`distribute-lft-neg-in_binary64`
6×	`distribute-rgt-neg-in_binary64`
6×	`sub-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	64
1	45	64
2	64	64
3	73	64
4	77	64
5	78	64
6	76	64

end248.0ms (5.5%)

Compiler: Compiled 356 to 196 computations (44.9% saved)

Iter	Nodes	Cost
0	8	10
1	17	10
2	32	10
3	73	10
4	175	10
5	216	10
6	290	10
7	411	10
8	431	10
9	481	10
10	484	10
11	504	10
12	453	10

Iter	Nodes	Cost
0	8	10
1	17	10
2	32	10
3	73	10
4	175	10
5	216	10
6	290	10
7	411	10
8	431	10
9	481	10
10	484	10
11	504	10
12	453	10

Details

analyze360.0ms (8%)

sample992.0ms (22.1%)

simplify24.0ms (0.5%)

prune2.0ms (0%)

localize5.0ms (0.1%)

series9.0ms (0.2%)

rewrite8.0ms (0.2%)

simplify53.0ms (1.2%)

prune42.0ms (0.9%)

localize6.0ms (0.1%)

series20.0ms (0.4%)

rewrite7.0ms (0.2%)

simplify82.0ms (1.8%)

prune54.0ms (1.2%)

localize9.0ms (0.2%)

series516.0ms (11.5%)

rewrite47.0ms (1%)

simplify250.0ms (5.6%)

prune475.0ms (10.6%)

localize14.0ms (0.3%)

series40.0ms (0.9%)

rewrite10.0ms (0.2%)

simplify89.0ms (2%)

prune619.0ms (13.8%)

regimes496.0ms (11.1%)

bsearch2.0ms (0%)

simplify4.0ms (0.1%)

end248.0ms (5.5%)

Profiling

Iter	Nodes	Cost
0	8	10
1	17	10
2	32	10
3	73	10
4	175	10
5	216	10
6	290	10
7	411	10
8	431	10
9	481	10
10	484	10
11	504	10
12	453	10