Details

analyze380.0ms (9%)

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)

sample898.0ms (21.2%)

Symmetry

(sort y z)

Results

785.0ms	8256×	body	128	valid
52.0ms	552×	body	128	invalid

Compiler

Compiled 32 to 23 computations (28.1% saved)

simplify24.0ms (0.6%)

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

2.6b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	2.6b	(.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
✓	2.4b	(.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)))

rewrite7.0ms (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:

6.0ms

(*.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

prune35.0ms (0.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	46	4	50
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	46	5	51

Error

0.0b

Counts

51 → 5

Alt Table

Status	Error	Program
✓	2.6b	(.f64 x (-.f64 1 (.f64 y z)))
▶	3.0b	(.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))))
	12.9b	(/.f64 (.f64 x (-.f64 1 (.f64 (.f64 y z) (.f64 y z)))) (+.f64 1 (*.f64 y z)))
	31.8b	(.f64 (sqrt.f64 (.f64 x (-.f64 1 (.f64 y z)))) (sqrt.f64 (.f64 x (-.f64 1 (*.f64 y z)))))
	5.1b	(-.f64 x (.f64 y (.f64 z x)))

Compiler

Compiled 852 to 428 computations (49.8% saved)

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.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))))
✓	0.6b	(.f64 x (.f64 (cbrt.f64 (-.f64 1 (.f64 y z))) (cbrt.f64 (-.f64 1 (.f64 y z)))))
✓	2.6b	(cbrt.f64 (-.f64 1 (*.f64 y z)))

series587.0ms (13.9%)

Counts

4 → 120

Calls

4 calls:

534.0ms	(.f64 x (.f64 (cbrt.f64 (-.f64 1 (.f64 y z))) (cbrt.f64 (-.f64 1 (.f64 y z)))))
24.0ms	(.f64 (cbrt.f64 (-.f64 1 (.f64 y z))) (cbrt.f64 (-.f64 1 (*.f64 y z))))
19.0ms	(cbrt.f64 (-.f64 1 (*.f64 y z)))
9.0ms	(.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))))

rewrite49.0ms (1.2%)

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))))
8.0ms	(.f64 (cbrt.f64 (-.f64 1 (.f64 y z))) (cbrt.f64 (-.f64 1 (*.f64 y z))))
8.0ms	(.f64 x (.f64 (cbrt.f64 (-.f64 1 (.f64 y z))) (cbrt.f64 (-.f64 1 (.f64 y z)))))
2.0ms	(cbrt.f64 (-.f64 1 (*.f64 y z)))

simplify302.0ms (7.1%)

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

prune445.0ms (10.5%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	434	1	435
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	435	5	440

Error

0.0b

Counts

440 → 5

Alt Table

Status	Error	Program
✓	2.6b	(.f64 x (-.f64 1 (.f64 y z)))
✓	3.0b	(.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))))
	31.8b	(.f64 (sqrt.f64 (.f64 x (-.f64 1 (.f64 y z)))) (sqrt.f64 (.f64 x (-.f64 1 (*.f64 y z)))))
	12.9b	(/.f64 (.f64 x (-.f64 1 (.f64 (.f64 y z) (.f64 y z)))) (fma.f64 y z 1))
▶	5.1b	(-.f64 x (.f64 y (.f64 z x)))

Compiler

Compiled 17767 to 10331 computations (41.9% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 x (.f64 y (.f64 z x)))
✓	6.3b	(.f64 y (.f64 z x))

series21.0ms (0.5%)

Counts

2 → 18

Calls

2 calls:

13.0ms	(.f64 y (.f64 z x))
8.0ms	(-.f64 x (.f64 y (.f64 z x)))

rewrite7.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`add-cbrt-cube_binary64`
7×	`add-exp-log_binary64`
7×	`pow1_binary64`
5×	`*-un-lft-identity_binary64`
5×	`add-sqr-sqrt_binary64`

Counts

2 → 40

Calls

2 calls:

3.0ms	(.f64 y (.f64 z x))
2.0ms	(-.f64 x (.f64 y (.f64 z x)))

simplify114.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

721×	`fma-def_binary64`
462×	`fma-neg_binary64`
392×	`distribute-rgt-neg-in_binary64`
378×	`distribute-lft-neg-in_binary64`
300×	`distribute-rgt-in_binary64`

Counts

58 → 55

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	80	682
1	195	637
2	585	609
3	1582	608
4	4260	608
5	4932	608
6	4986	608
7	4996	608
8	4794	608

prune33.0ms (0.8%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	54	1	55
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	54	6	60

Error

0.0b

Counts

60 → 6

Alt Table

Status	Error	Program
✓	2.6b	(.f64 x (-.f64 1 (.f64 y z)))
✓	3.0b	(.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))))
	31.8b	(.f64 (sqrt.f64 (.f64 x (-.f64 1 (.f64 y z)))) (sqrt.f64 (.f64 x (-.f64 1 (*.f64 y z)))))
	12.9b	(/.f64 (.f64 x (-.f64 1 (.f64 (.f64 y z) (.f64 y z)))) (fma.f64 y z 1))
✓	5.1b	(-.f64 x (.f64 y (.f64 z x)))
▶	5.4b	(-.f64 x (.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 y) (.f64 z x))))

Compiler

Compiled 889 to 314 computations (64.7% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(*.f64 (cbrt.f64 y) (cbrt.f64 y))
✓	0.6b	(cbrt.f64 y)
✓	2.3b	(.f64 (cbrt.f64 y) (.f64 z x))
✓	4.3b	(.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 y) (.f64 z x)))

series503.0ms (11.9%)

Counts

4 → 96

Calls

4 calls:

417.0ms	(.f64 (cbrt.f64 y) (.f64 z x))
35.0ms	(*.f64 (cbrt.f64 y) (cbrt.f64 y))
29.0ms	(cbrt.f64 y)
23.0ms	(.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 y) (.f64 z x)))

rewrite25.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

37×	`pow1_binary64`
32×	`add-exp-log_binary64`
23×	`add-sqr-sqrt_binary64`
22×	`cbrt-prod_binary64`
20×	`pow-prod-down_binary64`

Counts

4 → 108

Calls

4 calls:

8.0ms	(.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 y) (.f64 z x)))
7.0ms	(*.f64 (cbrt.f64 y) (cbrt.f64 y))
4.0ms	(.f64 (cbrt.f64 y) (.f64 z x))
1.0ms	(cbrt.f64 y)

simplify87.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

775×	`fma-def_binary64`
621×	`distribute-rgt-in_binary64`
464×	`*-commutative_binary64`
327×	`sqr-pow_binary64`
233×	`associate-l_binary64`

Counts

204 → 146

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	117	1885
1	239	1657
2	914	1619
3	1620	1605
4	2950	1511
5	4929	1511

prune118.0ms (2.8%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	180	2	182
Fresh	0	2	2
Picked	1	0	1
Done	0	3	3
Total	181	7	188

Error

Counts

188 → 7

Alt Table

Status	Error	Program
	5.5b	(-.f64 x (.f64 (.f64 (cbrt.f64 y) (.f64 (.f64 (cbrt.f64 (cbrt.f64 y)) (cbrt.f64 (cbrt.f64 y))) (cbrt.f64 (cbrt.f64 y)))) (.f64 (cbrt.f64 y) (.f64 z x))))
✓	3.0b	(.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))))
✓	2.6b	(.f64 x (-.f64 1 (.f64 y z)))
	5.4b	(-.f64 x (.f64 (cbrt.f64 y) (.f64 (cbrt.f64 y) (.f64 (cbrt.f64 y) (.f64 z x)))))
	31.8b	(.f64 (sqrt.f64 (.f64 x (-.f64 1 (.f64 y z)))) (sqrt.f64 (.f64 x (-.f64 1 (*.f64 y z)))))
	12.9b	(/.f64 (.f64 x (-.f64 1 (.f64 (.f64 y z) (.f64 y z)))) (fma.f64 y z 1))
✓	5.1b	(-.f64 x (.f64 y (.f64 z x)))

Compiler

Compiled 3483 to 894 computations (74.3% saved)

regimes262.0ms (6.2%)

Accuracy

Total 0.3b remaining (91%)

Threshold costs 0.3b (91%)

Counts

28 → 3

Compiler

Compiled 3607 to 2242 computations (37.8% saved)

bsearch1.0ms (0%)

Compiler: Compiled 10 to 7 computations (30% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

11×	`*-commutative_binary64`
8×	`+-commutative_binary64`
8×	`sub-neg_binary64`
6×	`neg-sub0_binary64`
6×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	59
1	36	59
2	50	59
3	64	59
4	72	59
5	76	59
6	77	59
7	76	59

end234.0ms (5.5%)

Compiler: Compiled 299 to 170 computations (43.1% 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

analyze380.0ms (9%)

sample898.0ms (21.2%)

simplify24.0ms (0.6%)

prune2.0ms (0%)

localize5.0ms (0.1%)

series9.0ms (0.2%)

rewrite7.0ms (0.2%)

simplify53.0ms (1.2%)

prune35.0ms (0.8%)

localize12.0ms (0.3%)

series587.0ms (13.9%)

rewrite49.0ms (1.2%)

simplify302.0ms (7.1%)

prune445.0ms (10.5%)

localize5.0ms (0.1%)

series21.0ms (0.5%)

rewrite7.0ms (0.2%)

simplify114.0ms (2.7%)

prune33.0ms (0.8%)

localize8.0ms (0.2%)

series503.0ms (11.9%)

rewrite25.0ms (0.6%)

simplify87.0ms (2.1%)

prune118.0ms (2.8%)

regimes262.0ms (6.2%)

bsearch1.0ms (0%)

simplify5.0ms (0.1%)

end234.0ms (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