Details

analyze284.0ms (4.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
25%	74.9%	0.2%	5
25%	74.9%	0.2%	6
25%	74.9%	0.2%	7
37.4%	62.4%	0.2%	8
56.1%	43.7%	0.2%	9
56.1%	43.7%	0.2%	10
56.1%	43.7%	0.2%	11
65.5%	34.3%	0.2%	12
76.4%	23.4%	0.2%	13
76.4%	23.4%	0.2%	14

Compiler

Compiled 14 to 9 computations (35.7% saved)

sample808.0ms (12.1%)

Infinites

5.1% of outputs are infinite.

Symmetry

(sort y t)

Results

712.0ms

8256×

body

128

valid

Compiler

Compiled 41 to 26 computations (36.6% saved)

simplify75.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

961×	`fma-neg_binary64`
750×	`fma-def_binary64`
246×	`distribute-rgt-in_binary64`
204×	`unsub-neg_binary64`
135×	`cancel-sign-sub-inv_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	15	13
2	35	13
3	88	13
4	231	13
5	568	13
6	1029	13
7	1474	13
8	1787	13
9	1744	13
10	1744	13
11	1905	13
12	1905	13
13	1862	13

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

5.7b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	5.7b	(/.f64 x (*.f64 (-.f64 y z) (-.f64 t z)))

Compiler

Compiled 39 to 24 computations (38.5% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (-.f64 y z) (-.f64 t z))
✓	5.7b	(/.f64 x (*.f64 (-.f64 y z) (-.f64 t z)))

series129.0ms (1.9%)

Counts

2 → 84

Calls

2 calls:

116.0ms	(/.f64 x (*.f64 (-.f64 y z) (-.f64 t z)))
13.0ms	(*.f64 (-.f64 y z) (-.f64 t z))

rewrite23.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`add-sqr-sqrt_binary64`
24×	`*-un-lft-identity_binary64`
20×	`add-cube-cbrt_binary64`
18×	`prod-diff_binary64`
13×	`distribute-lft-in_binary64`

Counts

2 → 89

Calls

2 calls:

11.0ms	(*.f64 (-.f64 y z) (-.f64 t z))
7.0ms	(/.f64 x (*.f64 (-.f64 y z) (-.f64 t z)))

simplify124.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

545×	`times-frac_binary64`
452×	`associate-/l*_binary64`
442×	`associate-/r*_binary64`
280×	`associate-l_binary64`
188×	`fma-def_binary64`

Counts

173 → 193

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	423	5441
1	1244	5124
2	4955	5124
3	5000	5124

prune173.0ms (2.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	186	7	193
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	187	7	194

Error

0.0b

Counts

194 → 7

Alt Table

Status	Error	Program
	11.0b	(/.f64 x (-.f64 (fma.f64 t y (.f64 z z)) (.f64 z (+.f64 y t))))
	19.8b	(.f64 (/.f64 x (.f64 (-.f64 (.f64 y y) (.f64 z z)) (-.f64 t z))) (+.f64 y z))
	22.4b	(/.f64 x (cbrt.f64 (pow.f64 (*.f64 (-.f64 t z) (-.f64 y z)) 3)))
	2.7b	(/.f64 1 (/.f64 (-.f64 y z) (/.f64 x (-.f64 t z))))
	5.8b	(/.f64 1 (/.f64 (*.f64 (-.f64 y z) (-.f64 t z)) x))
▶	2.7b	(*.f64 (/.f64 1 (-.f64 y z)) (/.f64 x (-.f64 t z)))
	3.2b	(/.f64 (/.f64 x (-.f64 y z)) (-.f64 t z))

Compiler

Compiled 5708 to 2113 computations (63% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1 (-.f64 y z))
✓	0.0b	(/.f64 x (-.f64 t z))
✓	2.7b	(*.f64 (/.f64 1 (-.f64 y z)) (/.f64 x (-.f64 t z)))

series137.0ms (2%)

Counts

3 → 96

Calls

3 calls:

112.0ms	(*.f64 (/.f64 1 (-.f64 y z)) (/.f64 x (-.f64 t z)))
16.0ms	(/.f64 x (-.f64 t z))
8.0ms	(/.f64 1 (-.f64 y z))

rewrite36.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

86×	`add-sqr-sqrt_binary64`
71×	`*-un-lft-identity_binary64`
67×	`times-frac_binary64`
41×	`add-cube-cbrt_binary64`
31×	`add-exp-log_binary64`

Counts

3 → 156

Calls

3 calls:

16.0ms	(*.f64 (/.f64 1 (-.f64 y z)) (/.f64 x (-.f64 t z)))
5.0ms	(/.f64 1 (-.f64 y z))
4.0ms	(/.f64 x (-.f64 t z))

simplify114.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

719×	`times-frac_binary64`
570×	`associate-/l*_binary64`
453×	`associate-/r*_binary64`
186×	`associate-*l/_binary64`
181×	`associate-*r/_binary64`

Counts

252 → 278

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	457	6865
1	1402	6443
2	5057	6443

prune210.0ms (3.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	275	3	278
Fresh	3	3	6
Picked	0	1	1
Done	0	0	0
Total	278	7	285

Error

Counts

285 → 7

Alt Table

Status	Error	Program
	11.0b	(/.f64 x (-.f64 (fma.f64 t y (.f64 z z)) (.f64 z (+.f64 y t))))
▶	2.6b	(/.f64 (/.f64 x (-.f64 t z)) (-.f64 y z))
	3.2b	(*.f64 (/.f64 x (-.f64 y z)) (/.f64 1 (-.f64 t z)))
	5.8b	(/.f64 1 (/.f64 (*.f64 (-.f64 y z) (-.f64 t z)) x))
✓	2.7b	(*.f64 (/.f64 1 (-.f64 y z)) (/.f64 x (-.f64 t z)))
	3.2b	(/.f64 (/.f64 x (-.f64 y z)) (-.f64 t z))
	3.2b	(.f64 (.f64 (cbrt.f64 (/.f64 1 (-.f64 y z))) (cbrt.f64 (/.f64 1 (-.f64 y z)))) (*.f64 (cbrt.f64 (/.f64 1 (-.f64 y z))) (/.f64 x (-.f64 t z))))

Compiler

Compiled 7443 to 2932 computations (60.6% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
	0.0b	(/.f64 x (-.f64 t z))
✓	2.6b	(/.f64 (/.f64 x (-.f64 t z)) (-.f64 y z))

series117.0ms (1.7%)

Counts

1 → 48

Calls

1 calls:

117.0ms

(/.f64 (/.f64 x (-.f64 t z)) (-.f64 y z))

rewrite28.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

195×	`times-frac_binary64`
157×	`*-un-lft-identity_binary64`
157×	`add-sqr-sqrt_binary64`
77×	`add-cube-cbrt_binary64`
40×	`distribute-lft-out--_binary64`

Counts

1 → 150

Calls

1 calls:

9.0ms

(/.f64 (/.f64 x (-.f64 t z)) (-.f64 y z))

simplify164.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

837×	`fma-def_binary64`
530×	`times-frac_binary64`
481×	`associate-/r*_binary64`
452×	`associate-/l*_binary64`
309×	`associate-/l/_binary64`

Counts

198 → 213

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	495	7582
1	1498	7346
2	4934	7270
3	5647	7270

prune182.0ms (2.7%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	269	1	270
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	270	7	277

Error

Counts

277 → 7

Alt Table

Status	Error	Program
	11.0b	(/.f64 x (-.f64 (fma.f64 t y (.f64 z z)) (.f64 z (+.f64 y t))))
▶	2.7b	(/.f64 (/.f64 1 1) (/.f64 (-.f64 y z) (/.f64 x (-.f64 t z))))
✓	2.6b	(/.f64 (/.f64 x (-.f64 t z)) (-.f64 y z))
	3.2b	(*.f64 (/.f64 x (-.f64 y z)) (/.f64 1 (-.f64 t z)))
✓	2.7b	(*.f64 (/.f64 1 (-.f64 y z)) (/.f64 x (-.f64 t z)))
	3.2b	(/.f64 (/.f64 x (-.f64 y z)) (-.f64 t z))
	3.2b	(.f64 (.f64 (cbrt.f64 (/.f64 1 (-.f64 y z))) (cbrt.f64 (/.f64 1 (-.f64 y z)))) (*.f64 (cbrt.f64 (/.f64 1 (-.f64 y z))) (/.f64 x (-.f64 t z))))

Compiler

Compiled 7649 to 2343 computations (69.4% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(/.f64 x (-.f64 t z))
✓	0.2b	(/.f64 (/.f64 1 1) (/.f64 (-.f64 y z) (/.f64 x (-.f64 t z))))
✓	2.6b	(/.f64 (-.f64 y z) (/.f64 x (-.f64 t z)))

series147.0ms (2.2%)

Counts

2 → 96

Calls

2 calls:

114.0ms	(/.f64 (/.f64 1 1) (/.f64 (-.f64 y z) (/.f64 x (-.f64 t z))))
33.0ms	(/.f64 (-.f64 y z) (/.f64 x (-.f64 t z)))

rewrite533.0ms (8%)

Algorithm

1×	rewrite-expression-head

Rules

5144×	`times-frac_binary64`
2881×	`*-un-lft-identity_binary64`
2881×	`add-sqr-sqrt_binary64`
1793×	`add-cube-cbrt_binary64`
544×	`distribute-lft-out--_binary64`

Counts

2 → 1745

Calls

2 calls:

45.0ms	(/.f64 (/.f64 1 1) (/.f64 (-.f64 y z) (/.f64 x (-.f64 t z))))
10.0ms	(/.f64 (-.f64 y z) (/.f64 x (-.f64 t z)))

simplify1.2s (17.8%)

Algorithm

1×	egg-herbie

Rules

678×	`associate-/r/_binary64`
661×	`times-frac_binary64`
230×	`associate-/l/_binary64`
167×	`fma-def_binary64`
142×	`distribute-rgt-in_binary64`

Counts

1841 → 1475

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	681	65445
1	1964	64719
2	5012	64719

prune1.1s (16.9%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	1532	0	1532
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	1532	7	1539

Error

Counts

1539 → 7

Alt Table

Status	Error	Program
	11.0b	(/.f64 x (-.f64 (fma.f64 t y (.f64 z z)) (.f64 z (+.f64 y t))))
✓	2.7b	(/.f64 (/.f64 1 1) (/.f64 (-.f64 y z) (/.f64 x (-.f64 t z))))
✓	2.6b	(/.f64 (/.f64 x (-.f64 t z)) (-.f64 y z))
	3.2b	(*.f64 (/.f64 x (-.f64 y z)) (/.f64 1 (-.f64 t z)))
✓	2.7b	(*.f64 (/.f64 1 (-.f64 y z)) (/.f64 x (-.f64 t z)))
	3.2b	(/.f64 (/.f64 x (-.f64 y z)) (-.f64 t z))
	3.2b	(.f64 (.f64 (cbrt.f64 (/.f64 1 (-.f64 y z))) (cbrt.f64 (/.f64 1 (-.f64 y z)))) (*.f64 (cbrt.f64 (/.f64 1 (-.f64 y z))) (/.f64 x (-.f64 t z))))

Compiler

Compiled 51600 to 19082 computations (63% saved)

regimes825.0ms (12.3%)

Accuracy

Total 1.6b remaining (99%)

Threshold costs 0b (0%)

Counts

132 → 3

Compiler

Compiled 15329 to 10015 computations (34.7% saved)

bsearch4.0ms (0.1%)

Compiler: Compiled 13 to 8 computations (38.5% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative_binary64`
3×	`+-commutative_binary64`
3×	`sub-neg_binary64`
1×	`*-lft-identity_binary64`
1×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	90
1	35	90
2	40	90
3	42	90
4	43	90
5	41	90

end225.0ms (3.4%)

Compiler: Compiled 377 to 169 computations (55.2% saved)

Details

analyze284.0ms (4.2%)

sample808.0ms (12.1%)

simplify75.0ms (1.1%)

prune1.0ms (0%)

localize6.0ms (0.1%)

series129.0ms (1.9%)

rewrite23.0ms (0.3%)

simplify124.0ms (1.9%)

prune173.0ms (2.6%)

localize7.0ms (0.1%)

series137.0ms (2%)

rewrite36.0ms (0.5%)

simplify114.0ms (1.7%)

prune210.0ms (3.1%)

localize7.0ms (0.1%)

series117.0ms (1.7%)

rewrite28.0ms (0.4%)

simplify164.0ms (2.5%)

prune182.0ms (2.7%)

localize8.0ms (0.1%)

series147.0ms (2.2%)

rewrite533.0ms (8%)

simplify1.2s (17.8%)

prune1.1s (16.9%)

regimes825.0ms (12.3%)

bsearch4.0ms (0.1%)

simplify5.0ms (0.1%)

end225.0ms (3.4%)

Profiling