Details

analyze350.0ms (6.8%)

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)

sample871.0ms (16.9%)

Symmetry

(sort y z)

Results

754.0ms	8256×	body	128	valid
56.0ms	580×	body	128	invalid

Compiler

Compiled 32 to 23 computations (28.1% saved)

simplify26.0ms (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

prune1.0ms (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

4.4b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	4.4b	(.f64 x (-.f64 1 (.f64 y z)))

Compiler

Compiled 30 to 21 computations (30% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	4.2b	(.f64 x (-.f64 1 (.f64 y z)))

series8.0ms (0.1%)

Counts

1 → 36

Calls

1 calls:

7.0ms

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

rewrite50.0ms (1%)

Algorithm

2×	batch-egg-rewrite

Rules

760×	`log1p-expm1-u_binary64`
760×	`expm1-log1p-u_binary64`
423×	`prod-diff_binary64`
83×	`add-sqr-sqrt_binary64`
76×	`add-cbrt-cube_binary64`

Counts

1 → 22

Calls

1 calls:

50.0ms

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	10
1	164	10
2	1947	10
3	5447	10
0	0	0
1	0	0

simplify37.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

428×	`fma-def_binary64`
125×	`fma-neg_binary64`
49×	`associate-l_binary64`
48×	`cancel-sign-sub-inv_binary64`
41×	`associate-r_binary64`

Counts

58 → 27

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	338
1	32	338
2	66	338
3	110	338
4	200	338
5	310	338
6	396	338
7	480	338
8	491	338
9	509	338
10	458	338

prune18.0ms (0.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	23	4	27
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	23	5	28

Error

0.1b

Counts

28 → 5

Alt Table

Status	Error	Program
	5.5b	(-.f64 x (.f64 y (.f64 z x)))
✓	4.4b	(.f64 x (-.f64 1 (.f64 y z)))
	35.0b	(pow.f64 (sqrt.f64 (.f64 x (-.f64 1 (.f64 y z)))) 2)
▶	5.5b	(pow.f64 (cbrt.f64 (.f64 x (-.f64 1 (.f64 y z)))) 3)
	15.9b	(/.f64 (.f64 (-.f64 1 (pow.f64 (.f64 y z) 2)) x) (+.f64 1 (*.f64 y z)))

Compiler

Compiled 397 to 235 computations (40.8% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.6b	(cbrt.f64 (.f64 x (-.f64 1 (.f64 y z))))
✓	0.8b	(pow.f64 (cbrt.f64 (.f64 x (-.f64 1 (.f64 y z)))) 3)
	4.2b	(.f64 x (-.f64 1 (.f64 y z)))

series1.2s (22.4%)

Counts

2 → 72

Calls

2 calls:

918.0ms	(pow.f64 (cbrt.f64 (.f64 x (-.f64 1 (.f64 y z)))) 3)
234.0ms	(cbrt.f64 (.f64 x (-.f64 1 (.f64 y z))))

rewrite113.0ms (2.2%)

Algorithm

2×	batch-egg-rewrite

Rules

482×	`log-prod_binary64`
433×	`prod-diff_binary64`
299×	`fma-udef_binary64`
175×	`expm1-udef_binary64`
174×	`log1p-udef_binary64`

Counts

2 → 80

Calls

2 calls:

111.0ms	(cbrt.f64 (.f64 x (-.f64 1 (.f64 y z))))
111.0ms	(pow.f64 (cbrt.f64 (.f64 x (-.f64 1 (.f64 y z)))) 3)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	22
1	212	22
2	2383	22
3	4899	22
4	4929	22
5	4923	22
0	0	0
1	0	0

simplify93.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

668×	`times-frac_binary64`
391×	`fma-def_binary64`
348×	`fma-neg_binary64`
344×	`associate-/l*_binary64`
311×	`cancel-sign-sub-inv_binary64`

Counts

152 → 149

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	142	2640
1	464	2536
2	1518	2418
3	4934	2418
4	5172	2418

prune204.0ms (4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	171	5	176
Fresh	1	2	3
Picked	1	0	1
Done	0	1	1
Total	173	8	181

Error

0.0b

Counts

181 → 8

Alt Table

Status	Error	Program
	38.2b	(pow.f64 (cbrt.f64 (neg.f64 (.f64 y (.f64 z x)))) 3)
	15.9b	(/.f64 (.f64 (-.f64 1 (pow.f64 (.f64 y z) 2)) x) (fma.f64 y z 1))
	5.5b	(-.f64 x (.f64 y (.f64 z x)))
▶	4.8b	(.f64 (pow.f64 (cbrt.f64 (-.f64 1 (.f64 y z))) 2) (.f64 (cbrt.f64 (-.f64 1 (.f64 y z))) x))
	33.1b	(.f64 (cbrt.f64 (.f64 x x)) (.f64 (cbrt.f64 x) (-.f64 1 (.f64 y z))))
	5.4b	(.f64 (cbrt.f64 x) (.f64 (cbrt.f64 (-.f64 1 (.f64 y z))) (pow.f64 (cbrt.f64 (.f64 x (-.f64 1 (*.f64 y z)))) 2)))
✓	4.4b	(.f64 x (-.f64 1 (.f64 y z)))
	35.0b	(pow.f64 (sqrt.f64 (.f64 x (-.f64 1 (.f64 y z)))) 2)

Compiler

Compiled 3908 to 2253 computations (42.3% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (cbrt.f64 (-.f64 1 (.f64 y z))) x)
✓	0.2b	(pow.f64 (cbrt.f64 (-.f64 1 (*.f64 y z))) 2)
✓	0.4b	(.f64 (pow.f64 (cbrt.f64 (-.f64 1 (.f64 y z))) 2) (.f64 (cbrt.f64 (-.f64 1 (.f64 y z))) x))
✓	4.3b	(cbrt.f64 (-.f64 1 (*.f64 y z)))

series581.0ms (11.3%)

Counts

4 → 120

Calls

4 calls:

434.0ms	(.f64 (cbrt.f64 (-.f64 1 (.f64 y z))) x)
123.0ms	(pow.f64 (cbrt.f64 (-.f64 1 (*.f64 y z))) 2)
15.0ms	(cbrt.f64 (-.f64 1 (*.f64 y z)))
8.0ms	(.f64 (pow.f64 (cbrt.f64 (-.f64 1 (.f64 y z))) 2) (.f64 (cbrt.f64 (-.f64 1 (.f64 y z))) x))

rewrite69.0ms (1.3%)

Algorithm

2×	batch-egg-rewrite

Rules

565×	`log-prod_binary64`
423×	`prod-diff_binary64`
200×	`expm1-udef_binary64`
199×	`log1p-udef_binary64`
178×	`log-pow_binary64`

Counts

4 → 92

Calls

4 calls:

67.0ms	(.f64 (cbrt.f64 (-.f64 1 (.f64 y z))) x)
67.0ms	(pow.f64 (cbrt.f64 (-.f64 1 (*.f64 y z))) 2)
67.0ms	(.f64 (pow.f64 (cbrt.f64 (-.f64 1 (.f64 y z))) 2) (.f64 (cbrt.f64 (-.f64 1 (.f64 y z))) x))
67.0ms	(cbrt.f64 (-.f64 1 (*.f64 y z)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	43
1	245	43
2	2690	43
3	5236	43
0	0	0
1	0	0

simplify230.0ms (4.5%)

Algorithm

1×	egg-herbie

Rules

780×	`cancel-sign-sub-inv_binary64`
342×	`distribute-neg-frac_binary64`
266×	`sub-neg_binary64`
254×	`associate-/r*_binary64`
226×	`fma-neg_binary64`

Counts

212 → 211

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	237	4094
1	847	3966
2	3168	3840
3	5426	3840

prune239.0ms (4.6%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	275	3	278
Fresh	3	3	6
Picked	0	1	1
Done	0	1	1
Total	278	8	286

Error

0.0b

Counts

286 → 8

Alt Table

Status	Error	Program
▶	4.9b	(.f64 (pow.f64 (cbrt.f64 (-.f64 1 (.f64 y z))) 2) (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (-.f64 1 (.f64 y z)))) 3) x))
✓	4.4b	(.f64 x (-.f64 1 (.f64 y z)))
	5.5b	(-.f64 x (.f64 y (.f64 z x)))
✓	4.8b	(.f64 (pow.f64 (cbrt.f64 (-.f64 1 (.f64 y z))) 2) (.f64 (cbrt.f64 (-.f64 1 (.f64 y z))) x))
	5.4b	(.f64 (cbrt.f64 x) (.f64 (cbrt.f64 (-.f64 1 (.f64 y z))) (pow.f64 (cbrt.f64 (.f64 x (-.f64 1 (*.f64 y z)))) 2)))
	13.7b	(.f64 (pow.f64 (cbrt.f64 (-.f64 1 (.f64 y z))) 2) (.f64 (/.f64 (cbrt.f64 (-.f64 1 (pow.f64 (.f64 y z) 2))) (cbrt.f64 (fma.f64 y z 1))) x))
	35.1b	(.f64 (pow.f64 (cbrt.f64 (-.f64 1 (.f64 y z))) 2) (pow.f64 (sqrt.f64 (.f64 (cbrt.f64 (-.f64 1 (.f64 y z))) x)) 2))
	38.2b	(pow.f64 (cbrt.f64 (neg.f64 (.f64 y (.f64 z x)))) 3)

Compiler

Compiled 9785 to 5836 computations (40.4% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(pow.f64 (cbrt.f64 (-.f64 1 (*.f64 y z))) 2)
✓	0.4b	(pow.f64 (cbrt.f64 (cbrt.f64 (-.f64 1 (*.f64 y z)))) 3)
✓	0.4b	(.f64 (pow.f64 (cbrt.f64 (-.f64 1 (.f64 y z))) 2) (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (-.f64 1 (.f64 y z)))) 3) x))
	4.3b	(cbrt.f64 (-.f64 1 (*.f64 y z)))

series37.0ms (0.7%)

Counts

2 → 60

Calls

2 calls:

27.0ms	(pow.f64 (cbrt.f64 (cbrt.f64 (-.f64 1 (*.f64 y z)))) 3)
9.0ms	(.f64 (pow.f64 (cbrt.f64 (-.f64 1 (.f64 y z))) 2) (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (-.f64 1 (.f64 y z)))) 3) x))

rewrite119.0ms (2.3%)

Algorithm

2×	batch-egg-rewrite

Rules

427×	`prod-diff_binary64`
306×	`fma-udef_binary64`
291×	`fma-def_binary64`
225×	`expm1-udef_binary64`
224×	`log1p-udef_binary64`

Counts

2 → 47

Calls

2 calls:

118.0ms	(pow.f64 (cbrt.f64 (cbrt.f64 (-.f64 1 (*.f64 y z)))) 3)
118.0ms	(.f64 (pow.f64 (cbrt.f64 (-.f64 1 (.f64 y z))) 2) (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (-.f64 1 (.f64 y z)))) 3) x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	19
1	290	19
2	3046	19
3	4831	19
4	4838	19
5	4948	19
0	0	0
1	0	0

simplify56.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

714×	`associate-/r*_binary64`
352×	`fma-def_binary64`
304×	`associate-*l/_binary64`
243×	`cancel-sign-sub-inv_binary64`
192×	`associate-/l/_binary64`

Counts

107 → 89

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	109	1570
1	352	1530
2	1575	1514
3	5021	1514

prune274.0ms (5.3%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	283	0	283
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	283	8	291

Error

0.0b

Counts

291 → 8

Alt Table

Status	Error	Program
✓	4.9b	(.f64 (pow.f64 (cbrt.f64 (-.f64 1 (.f64 y z))) 2) (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (-.f64 1 (.f64 y z)))) 3) x))
✓	4.4b	(.f64 x (-.f64 1 (.f64 y z)))
	5.5b	(-.f64 x (.f64 y (.f64 z x)))
✓	4.8b	(.f64 (pow.f64 (cbrt.f64 (-.f64 1 (.f64 y z))) 2) (.f64 (cbrt.f64 (-.f64 1 (.f64 y z))) x))
	5.4b	(.f64 (cbrt.f64 x) (.f64 (cbrt.f64 (-.f64 1 (.f64 y z))) (pow.f64 (cbrt.f64 (.f64 x (-.f64 1 (*.f64 y z)))) 2)))
	13.7b	(.f64 (pow.f64 (cbrt.f64 (-.f64 1 (.f64 y z))) 2) (.f64 (/.f64 (cbrt.f64 (-.f64 1 (pow.f64 (.f64 y z) 2))) (cbrt.f64 (fma.f64 y z 1))) x))
	35.1b	(.f64 (pow.f64 (cbrt.f64 (-.f64 1 (.f64 y z))) 2) (pow.f64 (sqrt.f64 (.f64 (cbrt.f64 (-.f64 1 (.f64 y z))) x)) 2))
	38.2b	(pow.f64 (cbrt.f64 (neg.f64 (.f64 y (.f64 z x)))) 3)

Compiler

Compiled 10542 to 6686 computations (36.6% saved)

regimes328.0ms (6.4%)

Accuracy

Total 0.4b remaining (91.7%)

Threshold costs 0.4b (91.7%)

Counts

26 → 3

Compiler

Compiled 3067 to 2197 computations (28.4% saved)

bsearch1.0ms (0%)

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

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

10×	`*-commutative_binary64`
7×	`+-commutative_binary64`
7×	`sub-neg_binary64`
6×	`distribute-rgt-neg-in_binary64`
6×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	46
1	35	46
2	54	46
3	65	46
4	72	46
5	74	46
6	73	46

end263.0ms (5.1%)

Compiler: Compiled 285 to 170 computations (40.4% 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	13	338
1	32	338
2	66	338
3	110	338
4	200	338
5	310	338
6	396	338
7	480	338
8	491	338
9	509	338
10	458	338

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	13	338
1	32	338
2	66	338
3	110	338
4	200	338
5	310	338
6	396	338
7	480	338
8	491	338
9	509	338
10	458	338

Details

analyze350.0ms (6.8%)

sample871.0ms (16.9%)

simplify26.0ms (0.5%)

prune1.0ms (0%)

localize4.0ms (0.1%)

series8.0ms (0.1%)

rewrite50.0ms (1%)

simplify37.0ms (0.7%)

prune18.0ms (0.3%)

localize9.0ms (0.2%)

series1.2s (22.4%)

rewrite113.0ms (2.2%)

simplify93.0ms (1.8%)

prune204.0ms (4%)

localize8.0ms (0.2%)

series581.0ms (11.3%)

rewrite69.0ms (1.3%)

simplify230.0ms (4.5%)

prune239.0ms (4.6%)

localize10.0ms (0.2%)

series37.0ms (0.7%)

rewrite119.0ms (2.3%)

simplify56.0ms (1.1%)

prune274.0ms (5.3%)

regimes328.0ms (6.4%)

bsearch1.0ms (0%)

simplify4.0ms (0.1%)

end263.0ms (5.1%)

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

Iter	Nodes	Cost
0	13	338
1	32	338
2	66	338
3	110	338
4	200	338
5	310	338
6	396	338
7	480	338
8	491	338
9	509	338
10	458	338