Details

analyze411.0ms (9.4%)

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)

sample983.0ms (22.4%)

Symmetry

(sort y z)

Results

833.0ms	8256×	body	128	valid
75.0ms	590×	body	128	invalid

Compiler

Compiled 32 to 23 computations (28.1% saved)

simplify23.0ms (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

prune7.0ms (0.2%)

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

3.8b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	3.8b	(.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))
✓	3.6b	(.f64 x (-.f64 1 (.f64 y z)))

series12.0ms (0.3%)

Counts

2 → 42

Calls

2 calls:

8.0ms	(.f64 x (-.f64 1 (.f64 y z)))
3.0ms	(-.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))

simplify69.0ms (1.6%)

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

prune62.0ms (1.4%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	73	5	78
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	74	5	79

Error

0.0b

Counts

79 → 5

Alt Table

Status	Error	Program
	4.2b	(.f64 x (.f64 (.f64 (cbrt.f64 (-.f64 1 (.f64 y z))) (cbrt.f64 (-.f64 1 (.f64 y z)))) (cbrt.f64 (-.f64 1 (.f64 y z)))))
	6.0b	(-.f64 x (.f64 y (.f64 z x)))
	14.9b	(.f64 x (cbrt.f64 (pow.f64 (-.f64 1 (.f64 y z)) 3)))
	11.8b	(/.f64 (.f64 x (-.f64 1 (.f64 (.f64 y z) (.f64 y z)))) (+.f64 1 (*.f64 y z)))
▶	3.8b	(+.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 1227 to 613 computations (50% saved)

localize11.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 1 1 (neg.f64 (*.f64 z y)))
✓	3.6b	(.f64 (fma.f64 1 1 (neg.f64 (.f64 z y))) x)
✓	51.9b	(fma.f64 (neg.f64 z) y (*.f64 z y))

series20.0ms (0.5%)

Counts

3 → 84

Calls

3 calls:

9.0ms	(.f64 (fma.f64 1 1 (neg.f64 (.f64 z y))) x)
8.0ms	(fma.f64 (neg.f64 z) y (*.f64 z y))
4.0ms	(fma.f64 1 1 (neg.f64 (*.f64 z y)))

rewrite7.0ms (0.2%)

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:

5.0ms	(.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)))

simplify69.0ms (1.6%)

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

prune76.0ms (1.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	78	1	79
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	78	6	84

Error

0.0b

Counts

84 → 6

Alt Table

Status	Error	Program
▶	4.2b	(.f64 x (.f64 (.f64 (cbrt.f64 (-.f64 1 (.f64 y z))) (cbrt.f64 (-.f64 1 (.f64 y z)))) (cbrt.f64 (-.f64 1 (.f64 y z)))))
	6.0b	(-.f64 x (.f64 y (.f64 z x)))
	14.9b	(.f64 x (cbrt.f64 (pow.f64 (-.f64 1 (.f64 y z)) 3)))
	5.0b	(+.f64 (.f64 (.f64 (-.f64 1 (.f64 y z)) (.f64 (cbrt.f64 x) (cbrt.f64 x))) (cbrt.f64 x)) (.f64 (fma.f64 (neg.f64 z) y (.f64 z y)) x))
	11.8b	(/.f64 (.f64 x (-.f64 1 (.f64 (.f64 y z) (.f64 y z)))) (+.f64 1 (*.f64 y z)))
✓	3.8b	(+.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 2008 to 730 computations (63.6% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (.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))))
✓	3.6b	(.f64 x (.f64 (.f64 (cbrt.f64 (-.f64 1 (.f64 y z))) (cbrt.f64 (-.f64 1 (.f64 y z)))) (cbrt.f64 (-.f64 1 (.f64 y z)))))
✓	3.8b	(cbrt.f64 (-.f64 1 (*.f64 y z)))

series59.0ms (1.3%)

Counts

4 → 108

Calls

4 calls:

26.0ms	(.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 x (.f64 (.f64 (cbrt.f64 (-.f64 1 (.f64 y z))) (cbrt.f64 (-.f64 1 (.f64 y z)))) (cbrt.f64 (-.f64 1 (.f64 y z)))))
4.0ms	(.f64 (.f64 (cbrt.f64 (-.f64 1 (.f64 y z))) (cbrt.f64 (-.f64 1 (.f64 y z)))) (cbrt.f64 (-.f64 1 (*.f64 y z))))

rewrite67.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

122×	`cbrt-div_binary64`
61×	`flip--_binary64`
61×	`flip3--_binary64`
60×	`frac-times_binary64`
44×	`associate-*r/_binary64`

Counts

4 → 178

Calls

4 calls:

17.0ms	(.f64 x (.f64 (.f64 (cbrt.f64 (-.f64 1 (.f64 y z))) (cbrt.f64 (-.f64 1 (.f64 y z)))) (cbrt.f64 (-.f64 1 (.f64 y z)))))
14.0ms	(.f64 (.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 (cbrt.f64 (-.f64 1 (.f64 y z))) (cbrt.f64 (-.f64 1 (*.f64 y z))))
2.0ms	(cbrt.f64 (-.f64 1 (*.f64 y z)))

simplify166.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

785×	`cancel-sign-sub-inv_binary64`
288×	`associate-/r*_binary64`
275×	`associate-r_binary64`
260×	`associate-l_binary64`
253×	`distribute-neg-frac_binary64`

Counts

286 → 323

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	351	7880
1	867	7291
2	3041	6921
3	5171	6921

prune453.0ms (10.3%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	437	0	437
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	437	6	443

Error

0.0b

Counts

443 → 6

Alt Table

Status	Error	Program
✓	4.2b	(.f64 x (.f64 (.f64 (cbrt.f64 (-.f64 1 (.f64 y z))) (cbrt.f64 (-.f64 1 (.f64 y z)))) (cbrt.f64 (-.f64 1 (.f64 y z)))))
	6.0b	(-.f64 x (.f64 y (.f64 z x)))
	14.9b	(.f64 x (cbrt.f64 (pow.f64 (-.f64 1 (.f64 y z)) 3)))
▶	5.0b	(+.f64 (.f64 (.f64 (-.f64 1 (.f64 y z)) (.f64 (cbrt.f64 x) (cbrt.f64 x))) (cbrt.f64 x)) (.f64 (fma.f64 (neg.f64 z) y (.f64 z y)) x))
	11.8b	(/.f64 (.f64 x (-.f64 1 (.f64 (.f64 y z) (.f64 y z)))) (+.f64 1 (*.f64 y z)))
✓	3.8b	(+.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 17800 to 10105 computations (43.2% saved)

localize14.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.6b	(cbrt.f64 x)
✓	0.8b	(.f64 (.f64 (-.f64 1 (.f64 y z)) (.f64 (cbrt.f64 x) (cbrt.f64 x))) (cbrt.f64 x))
✓	3.2b	(.f64 (-.f64 1 (.f64 y z)) (*.f64 (cbrt.f64 x) (cbrt.f64 x)))
	51.9b	(fma.f64 (neg.f64 z) y (*.f64 z y))

series249.0ms (5.7%)

Counts

3 → 84

Calls

3 calls:

197.0ms	(.f64 (-.f64 1 (.f64 y z)) (*.f64 (cbrt.f64 x) (cbrt.f64 x)))
30.0ms	(cbrt.f64 x)
22.0ms	(.f64 (.f64 (-.f64 1 (.f64 y z)) (.f64 (cbrt.f64 x) (cbrt.f64 x))) (cbrt.f64 x))

rewrite20.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`add-exp-log_binary64`
17×	`pow1_binary64`
10×	`add-cbrt-cube_binary64`
9×	`cbrt-unprod_binary64`
9×	`prod-exp_binary64`

Counts

3 → 64

Calls

3 calls:

9.0ms	(.f64 (.f64 (-.f64 1 (.f64 y z)) (.f64 (cbrt.f64 x) (cbrt.f64 x))) (cbrt.f64 x))
7.0ms	(.f64 (-.f64 1 (.f64 y z)) (*.f64 (cbrt.f64 x) (cbrt.f64 x)))
1.0ms	(cbrt.f64 x)

simplify76.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

554×	`associate-+l+_binary64`
480×	`unswap-sqr_binary64`
433×	`*-commutative_binary64`
198×	`distribute-rgt-in_binary64`
197×	`distribute-lft-in_binary64`

Counts

148 → 107

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	103	2170
1	255	1766
2	918	1681
3	2168	1679
4	4970	1679

prune98.0ms (2.2%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	162	0	162
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	162	6	168

Error

0.0b

Counts

168 → 6

Alt Table

Status	Error	Program
✓	4.2b	(.f64 x (.f64 (.f64 (cbrt.f64 (-.f64 1 (.f64 y z))) (cbrt.f64 (-.f64 1 (.f64 y z)))) (cbrt.f64 (-.f64 1 (.f64 y z)))))
	6.0b	(-.f64 x (.f64 y (.f64 z x)))
	14.9b	(.f64 x (cbrt.f64 (pow.f64 (-.f64 1 (.f64 y z)) 3)))
✓	5.0b	(+.f64 (.f64 (.f64 (-.f64 1 (.f64 y z)) (.f64 (cbrt.f64 x) (cbrt.f64 x))) (cbrt.f64 x)) (.f64 (fma.f64 (neg.f64 z) y (.f64 z y)) x))
	11.8b	(/.f64 (.f64 x (-.f64 1 (.f64 (.f64 y z) (.f64 y z)))) (+.f64 1 (*.f64 y z)))
✓	3.8b	(+.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 4711 to 1427 computations (69.7% saved)

regimes1.1s (26.2%)

Accuracy

Total 0.1b remaining (71%)

Threshold costs 0.1b (71%)

Counts

88 → 3

Compiler

Compiled 11320 to 7666 computations (32.3% saved)

bsearch2.0ms (0.1%)

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

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

12×	`*-commutative_binary64`
9×	`+-commutative_binary64`
8×	`distribute-rgt-neg-in_binary64`
8×	`sub-neg_binary64`
7×	`distribute-lft-neg-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	54
1	45	54
2	67	54
3	83	54
4	89	54
5	90	54
6	90	54

end263.0ms (6%)

Compiler: Compiled 273 to 151 computations (44.7% 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

analyze411.0ms (9.4%)

sample983.0ms (22.4%)

simplify23.0ms (0.5%)

prune7.0ms (0.2%)

localize5.0ms (0.1%)

series12.0ms (0.3%)

rewrite9.0ms (0.2%)

simplify69.0ms (1.6%)

prune62.0ms (1.4%)

localize11.0ms (0.2%)

series20.0ms (0.5%)

rewrite7.0ms (0.2%)

simplify69.0ms (1.6%)

prune76.0ms (1.7%)

localize8.0ms (0.2%)

series59.0ms (1.3%)

rewrite67.0ms (1.5%)

simplify166.0ms (3.8%)

prune453.0ms (10.3%)

localize14.0ms (0.3%)

series249.0ms (5.7%)

rewrite20.0ms (0.5%)

simplify76.0ms (1.7%)

prune98.0ms (2.2%)

regimes1.1s (26.2%)

bsearch2.0ms (0.1%)

simplify4.0ms (0.1%)

end263.0ms (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