Details

analyze393.0ms (10.8%)

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)

sample928.0ms (25.5%)

Symmetry

(sort y z)

Results

792.0ms	8256×	body	128	valid
64.0ms	641×	body	128	invalid

Compiler

Compiled 32 to 23 computations (28.1% saved)

simplify22.0ms (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

3.1b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	3.1b	(.f64 x (-.f64 1 (.f64 y z)))

Compiler

Compiled 30 to 21 computations (30% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 1 (*.f64 y z))
✓	2.9b	(.f64 x (-.f64 1 (.f64 y z)))

series14.0ms (0.4%)

Counts

2 → 42

Calls

2 calls:

10.0ms	(.f64 x (-.f64 1 (.f64 y z)))
4.0ms	(-.f64 1 (*.f64 y z))

rewrite9.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-sqr-sqrt_binary64`
9×	`prod-diff_binary64`
8×	`*-un-lft-identity_binary64`
8×	`add-cube-cbrt_binary64`
5×	`distribute-lft-in_binary64`

Counts

2 → 52

Calls

2 calls:

4.0ms	(.f64 x (-.f64 1 (.f64 y z)))
2.0ms	(-.f64 1 (*.f64 y z))

simplify64.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

900×	`fma-def_binary64`
608×	`distribute-neg-out_binary64`
601×	`unsub-neg_binary64`
328×	`associate-l_binary64`
264×	`*-commutative_binary64`

Counts

94 → 78

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	81	1122
1	163	1031
2	520	977
3	1456	950
4	2828	950
5	5227	950

prune67.0ms (1.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	73	5	78
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	73	6	79

Error

0.0b

Counts

79 → 6

Alt Table

Status	Error	Program
✓	3.1b	(.f64 x (-.f64 1 (.f64 y z)))
	4.9b	(-.f64 x (.f64 y (.f64 z x)))
	13.9b	(.f64 (.f64 x (sqrt.f64 (-.f64 1 (.f64 y z)))) (sqrt.f64 (-.f64 1 (.f64 y z))))
	34.5b	(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (-.f64 1 (*.f64 y z))))
	13.6b	(/.f64 (.f64 x (-.f64 1 (.f64 (.f64 y z) (.f64 y z)))) (+.f64 1 (*.f64 y z)))
▶	3.1b	(+.f64 (.f64 (fma.f64 1 1 (neg.f64 (.f64 z y))) x) (.f64 (fma.f64 (neg.f64 z) y (.f64 z y)) x))

Compiler

Compiled 1225 to 610 computations (50.2% saved)

localize14.0ms (0.4%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 1 1 (neg.f64 (*.f64 z y)))
✓	2.9b	(.f64 (fma.f64 1 1 (neg.f64 (.f64 z y))) x)
✓	52.9b	(fma.f64 (neg.f64 z) y (*.f64 z y))

series25.0ms (0.7%)

Counts

3 → 84

Calls

3 calls:

13.0ms	(.f64 (fma.f64 1 1 (neg.f64 (.f64 z y))) x)
7.0ms	(fma.f64 (neg.f64 z) y (*.f64 z y))
4.0ms	(fma.f64 1 1 (neg.f64 (*.f64 z y)))

rewrite5.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 40

Calls

3 calls:

3.0ms	(.f64 (fma.f64 1 1 (neg.f64 (.f64 z y))) x)
0.0ms	(fma.f64 (neg.f64 z) y (*.f64 z y))
0.0ms	(fma.f64 1 1 (neg.f64 (*.f64 z y)))

simplify70.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

712×	`fma-def_binary64`
629×	`distribute-rgt-neg-out_binary64`
627×	`distribute-rgt-in_binary64`
578×	`distribute-lft-in_binary64`
387×	`distribute-neg-out_binary64`

Counts

124 → 79

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	64	1027
1	114	945
2	299	897
3	884	897
4	2991	897
5	5217	897

prune70.0ms (1.9%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	79	0	79
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	79	6	85

Error

0.0b

Counts

85 → 6

Alt Table

Status	Error	Program
✓	3.1b	(.f64 x (-.f64 1 (.f64 y z)))
▶	4.9b	(-.f64 x (.f64 y (.f64 z x)))
	13.9b	(.f64 (.f64 x (sqrt.f64 (-.f64 1 (.f64 y z)))) (sqrt.f64 (-.f64 1 (.f64 y z))))
	34.5b	(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (-.f64 1 (*.f64 y z))))
	13.6b	(/.f64 (.f64 x (-.f64 1 (.f64 (.f64 y z) (.f64 y z)))) (+.f64 1 (*.f64 y z)))
✓	3.1b	(+.f64 (.f64 (fma.f64 1 1 (neg.f64 (.f64 z y))) x) (.f64 (fma.f64 (neg.f64 z) y (.f64 z y)) x))

Compiler

Compiled 1952 to 697 computations (64.3% saved)

localize7.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	5.7b	(.f64 y (.f64 z x))

series9.0ms (0.2%)

Counts

1 → 0

Calls

1 calls:

9.0ms

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

rewrite5.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`add-cbrt-cube_binary64`
6×	`add-exp-log_binary64`
6×	`pow1_binary64`
3×	`associate-l_binary64`
3×	`cbrt-unprod_binary64`

Counts

1 → 20

Calls

1 calls:

4.0ms

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

simplify76.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

580×	`log-div_binary64`
514×	`associate-/l*_binary64`
411×	`*-commutative_binary64`
409×	`associate-l_binary64`
339×	`cube-div_binary64`

Counts

20 → 20

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	38	219
1	87	174
2	275	174
3	770	174
4	976	174
5	1185	174
6	1422	174
7	1902	174
8	3020	174
9	4714	174
10	4982	174

prune18.0ms (0.5%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	18	2	20
Fresh	0	3	3
Picked	0	1	1
Done	1	1	2
Total	19	7	26

Error

0.0b

Counts

26 → 7

Alt Table

Status	Error	Program
✓	4.9b	(-.f64 x (.f64 y (.f64 z x)))
	46.8b	(-.f64 x (.f64 (sqrt.f64 y) (.f64 (sqrt.f64 y) (*.f64 z x))))
▶	5.3b	(-.f64 x (.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 y) (.f64 z x))))
	13.9b	(.f64 (.f64 x (sqrt.f64 (-.f64 1 (.f64 y z)))) (sqrt.f64 (-.f64 1 (.f64 y z))))
	34.5b	(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (-.f64 1 (*.f64 y z))))
	13.6b	(/.f64 (.f64 x (-.f64 1 (.f64 (.f64 y z) (.f64 y z)))) (+.f64 1 (*.f64 y z)))
✓	3.1b	(+.f64 (.f64 (fma.f64 1 1 (neg.f64 (.f64 z y))) x) (.f64 (fma.f64 (neg.f64 z) y (.f64 z y)) x))

Compiler

Compiled 447 to 201 computations (55% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(*.f64 (cbrt.f64 y) (cbrt.f64 y))
✓	0.5b	(cbrt.f64 y)
✓	2.6b	(.f64 (cbrt.f64 y) (.f64 z x))
✓	3.2b	(.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 y) (.f64 z x)))

series519.0ms (14.3%)

Counts

4 → 96

Calls

4 calls:

431.0ms	(.f64 (cbrt.f64 y) (.f64 z x))
38.0ms	(*.f64 (cbrt.f64 y) (cbrt.f64 y))
29.0ms	(cbrt.f64 y)
21.0ms	(.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 y) (.f64 z x)))

rewrite25.0ms (0.7%)

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

simplify88.0ms (2.4%)

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

prune196.0ms (5.4%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	179	3	182
Fresh	1	3	4
Picked	1	0	1
Done	0	2	2
Total	181	8	189

Error

0.0b

Counts

189 → 8

Alt Table

Status	Error	Program
	13.9b	(.f64 (.f64 x (sqrt.f64 (-.f64 1 (.f64 y z)))) (sqrt.f64 (-.f64 1 (.f64 y z))))
	16.3b	(-.f64 x (.f64 (cbrt.f64 (.f64 y y)) (.f64 (cbrt.f64 y) (.f64 z x))))
	5.4b	(-.f64 x (.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y))) (.f64 (cbrt.f64 (cbrt.f64 y)) (.f64 z x)))))
✓	3.1b	(+.f64 (.f64 (fma.f64 1 1 (neg.f64 (.f64 z y))) x) (.f64 (fma.f64 (neg.f64 z) y (.f64 z y)) x))
	18.8b	(-.f64 x (cbrt.f64 (.f64 (.f64 (.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 y) (.f64 z x))) (.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 y) (.f64 z x)))) (.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 y) (.f64 z x))))))
✓	4.9b	(-.f64 x (.f64 y (.f64 z x)))
	46.8b	(-.f64 x (.f64 (sqrt.f64 y) (.f64 (sqrt.f64 y) (*.f64 z x))))
	13.6b	(/.f64 (.f64 x (-.f64 1 (.f64 (.f64 y z) (.f64 y z)))) (+.f64 1 (*.f64 y z)))

Compiler

Compiled 3525 to 904 computations (74.4% saved)

regimes647.0ms (17.8%)

Accuracy

Total 1.9b remaining (98.5%)

Threshold costs 0b (0%)

Counts

62 → 3

Compiler

Compiled 7598 to 4416 computations (41.9% saved)

bsearch38.0ms (1%)

Steps

Iters	Range		Point
6	1.9691331608356181e-75	1.3219225737822803e-74	2.617901184839269e-75
7	-1.117129344981238e+224	-1.3816249392849155e+222	-4.934776551119867e+222

Compiler

Compiled 4 to 3 computations (25% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

19×	`*-commutative_binary64`
15×	`+-commutative_binary64`
15×	`distribute-rgt-neg-in_binary64`
15×	`sub-neg_binary64`
12×	`distribute-lft-neg-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	54
1	45	54
2	79	54
3	110	54
4	132	54
5	139	54
6	140	54
7	140	54

end315.0ms (8.6%)

Compiler: Compiled 325 to 168 computations (48.3% 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

analyze393.0ms (10.8%)

sample928.0ms (25.5%)

simplify22.0ms (0.6%)

prune2.0ms (0%)

localize5.0ms (0.1%)

series14.0ms (0.4%)

rewrite9.0ms (0.2%)

simplify64.0ms (1.7%)

prune67.0ms (1.8%)

localize14.0ms (0.4%)

series25.0ms (0.7%)

rewrite5.0ms (0.1%)

simplify70.0ms (1.9%)

prune70.0ms (1.9%)

localize7.0ms (0.2%)

series9.0ms (0.2%)

rewrite5.0ms (0.1%)

simplify76.0ms (2.1%)

prune18.0ms (0.5%)

localize10.0ms (0.3%)

series519.0ms (14.3%)

rewrite25.0ms (0.7%)

simplify88.0ms (2.4%)

prune196.0ms (5.4%)

regimes647.0ms (17.8%)

bsearch38.0ms (1%)

simplify5.0ms (0.1%)

end315.0ms (8.6%)

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